Documentation Verification Report

Mon_

📁 Source: Mathlib/CategoryTheory/Monoidal/Mon_.lean

Statistics

MetricCount
DefinitionsAddMon, addMonToLaxMonoidal, addMonToLaxMonoidalObj, addUnitIso, counitIso, counitIsoAux, instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj, laxMonoidalToAddMon, hom, mk', X, addMon, comp, equivLaxMonoidalFunctorPUnit, forget, homInhabited, id, instAddMonObjTensorObj, instCategory, instInhabited, instMonoidalForget, instSymmetricCategory, mkIso, mkIso', monMonoidal, monMonoidalStruct, trivial, uniqueHomFromTrivial, AddMonObj, add, instTensorAddUnit, ofIso, instTensorObj, termζ, termσ, zero, «termζ[_]», «termσ[_]», mapAddMon, mapMon, mapAddMon, mapMon, addMonObj, mapAddMon, mapMon, monObj, addMonObjObj, instBraidedMonMapAddMon, instBraidedMonMapMon, instLaxBraidedMonMapAddMon, instLaxBraidedMonMapMon, instLaxMonoidalMonMapAddMon, instLaxMonoidalMonMapMon, instMonoidalMonMapAddMon, instMonoidalMonMapMon, mapAddMon, mapAddMonCompIso, mapAddMonFunctor, mapAddMonIdIso, mapAddMonNatIso, mapAddMonNatTrans, mapMon, mapMonCompIso, mapMonFunctor, mapMonIdIso, mapMonNatIso, mapMonNatTrans, monObjObj, IsAddMonHom, IsCommAddMonObj, IsCommMonObj, IsMonHom, Mon, counitIso, counitIsoAux, instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj, laxMonoidalToMon, monToLaxMonoidal, monToLaxMonoidalObj, unitIso, hom, mk', X, comp, equivLaxMonoidalFunctorPUnit, forget, homInhabited, id, instCategory, instInhabited, instMonObjTensorObj, instMonoidalForget, instSymmetricCategory, mkIso, mkIso', mon, monMonoidal, monMonoidalStruct, trivial, uniqueHomFromTrivial, MonObj, instTensorUnit, mul, ofIso, one, instTensorObj, termη, termμ, «termη[_]», «termμ[_]»
110
TheoremsaddMonToLaxMonoidalObj_map, addMonToLaxMonoidalObj_obj, addMonToLaxMonoidalObj_ε, addMonToLaxMonoidalObj_μ, addMonToLaxMonoidal_laxMonoidalToAddMon_obj_add, addMonToLaxMonoidal_laxMonoidalToAddMon_obj_zero, addMonToLaxMonoidal_map_hom_app, addMonToLaxMonoidal_obj, addUnitIso_hom_app_hom_app, addUnitIso_inv_app_hom_app, counitIsoAux_hom, counitIsoAux_inv, counitIso_hom_app_hom, counitIso_inv_app_hom, isAddMonHom_counitIsoAux, laxMonoidalToAddMon_map, laxMonoidalToAddMon_obj, ext, ext', ext'_iff, ext_iff, isAddMonHom_hom, add_def, associator_hom_hom, associator_neg_hom, braiding_hom_hom, braiding_neg_hom, comp_hom, comp_hom', comp_hom'_assoc, equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, equivLaxMonoidalFunctorPUnit_functor_map_hom, equivLaxMonoidalFunctorPUnit_functor_obj_X, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero, equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, equivLaxMonoidalFunctorPUnit_inverse_obj_map, equivLaxMonoidalFunctorPUnit_inverse_obj_obj, equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, forget_faithful, forget_map, forget_obj, forget_δ, forget_ε, forget_η, forget_μ, hom_injective, id_hom, id_hom', instHasInitial, instIsAddMonHomHom, instIsIsoHom, instIsIsoHomOfMapForget, instReflectsIsomorphismsForget, leftUnitor_hom_hom, leftUnitor_neg_hom, mkIso'_hom_hom, mkIso'_inv_hom, mkIso_hom_hom, mkIso_inv_hom, monMonoidalStruct_tensorHom_hom, monMonoidalStruct_tensorObj_X, rightUnitor_hom_hom, rightUnitor_neg_hom, tensorAddUnit_X, tensorAddUnit_add, tensorAddUnit_zero, tensorObj_add, tensorObj_zero, tensor_add, tensor_zero, trivial_X, trivial_addMon_add, trivial_addMon_zero, uniqueHomFromTrivial_default_hom, whiskerLeft_hom, whiskerRight_hom, zero_def, AddMon_tensor_add_assoc, AddMon_tensor_add_zero, AddMon_tensor_zero_add, add_add_add_comm, add_add_add_comm', add_add_add_comm'_assoc, add_add_add_comm_assoc, add_assoc, add_assoc_assoc, add_assoc_flip, add_assoc_flip_assoc, add_associator, add_braiding, add_def, add_leftUnitor, add_rightUnitor, add_zero, add_zero_assoc, add_zero_hom, add_zero_hom_assoc, ext, ext_iff, instIsAddMonHomHomAssociator, instIsAddMonHomHomBraiding, instIsAddMonHomHomLeftUnitor, instIsAddMonHomHomRightUnitor, instIsAddMonHomId, instIsAddMonHomTensorHom, instIsAddMonHomWhiskerLeft, instIsAddMonHomWhiskerRight, ofIso_add, ofIso_zero, add_def, zero_def, zero_add, zero_add_assoc, zero_add_hom, zero_add_hom_assoc, zero_associator, zero_braiding, zero_def, zero_leftUnitor, zero_rightUnitor, mapAddMon_counit, mapAddMon_unit, mapMon_counit, mapMon_unit, mapAddMon_counitIso, mapAddMon_functor, mapAddMon_inverse, mapAddMon_unitIso, mapMon_counitIso, mapMon_functor, mapMon_inverse, mapMon_unitIso, mapAddMon, mapMon, mapAddMon, mapMon, addMonObj_add, addMonObj_zero, isAddMonHom_preimage, isMonHom_preimage, mapAddMon_preimage_hom, mapMon_preimage_hom, monObj_mul, monObj_one, comp_mapAddMon_add, comp_mapAddMon_zero, comp_mapMon_mul, comp_mapMon_one, essImage_mapAddMon, essImage_mapMon, id_mapAddMon_add, id_mapAddMon_zero, id_mapMon_mul, id_mapMon_one, instIsAddMonHomε, instIsAddMonHomμ, instIsMonHomε, instIsMonHomμ, instIsAddMonHom, instIsMonHom, mapAddMonCompIso_hom_app_hom, mapAddMonCompIso_inv_app_hom, mapAddMonFunctor_map_app_hom, mapAddMonFunctor_obj, mapAddMonIdIso_hom_app_hom, mapAddMonIdIso_inv_app_hom, mapAddMonNatIso_hom_app_hom, mapAddMonNatIso_inv_app_hom, mapAddMonNatTrans_app_hom, mapAddMon_map_hom, mapAddMon_obj_X, mapAddMon_obj_addMon_add, mapAddMon_obj_addMon_zero, mapMonCompIso_hom_app_hom, mapMonCompIso_inv_app_hom, mapMonFunctor_map_app_hom, mapMonFunctor_obj, mapMonIdIso_hom_app_hom, mapMonIdIso_inv_app_hom, mapMonNatIso_hom_app_hom, mapMonNatIso_inv_app_hom, mapMonNatTrans_app_hom, mapMon_map_hom, mapMon_obj_X, mapMon_obj_mon_mul, mapMon_obj_mon_one, ζ_def, ζ_def_assoc, η_def, η_def_assoc, μ_def, μ_def_assoc, σ_def, σ_def_assoc, add_hom, add_hom_assoc, zero_hom, zero_hom_assoc, add_comm, add_comm', add_comm'_assoc, instTensorAddUnit, instTensorUnit, mul_comm, mul_comm', mul_comm'_assoc, mul_comm_assoc, mul_hom, mul_hom_assoc, one_hom, one_hom_assoc, add_assoc_hom, add_assoc_hom_assoc, add_assoc_neg, add_assoc_neg_assoc, associator_hom_comp_tensorHom_tensorHom, associator_hom_comp_tensorHom_tensorHom_assoc, associator_hom_comp_tensorHom_tensorHom_comp, associator_hom_comp_tensorHom_tensorHom_comp_assoc, associator_inv_comp_tensorHom_tensorHom, associator_inv_comp_tensorHom_tensorHom_assoc, associator_inv_comp_tensorHom_tensorHom_comp, associator_inv_comp_tensorHom_tensorHom_comp_assoc, eq_add_zero, eq_mul_one, eq_one_mul, eq_zero_add, leftUnitor_inv_one_tensor_mul, leftUnitor_inv_one_tensor_mul_assoc, leftUnitor_neg_zero_tensor_add, leftUnitor_neg_zero_tensor_add_assoc, mul_assoc_hom, mul_assoc_hom_assoc, mul_assoc_inv, mul_assoc_inv_assoc, rightUnitor_inv_tensor_one_mul, rightUnitor_inv_tensor_one_mul_assoc, rightUnitor_neg_tensor_zero_add, rightUnitor_neg_tensor_zero_add_assoc, counitIsoAux_hom, counitIsoAux_inv, counitIso_hom_app_hom, counitIso_inv_app_hom, isMonHom_counitIsoAux, laxMonoidalToMon_map, laxMonoidalToMon_obj, monToLaxMonoidalObj_map, monToLaxMonoidalObj_obj, monToLaxMonoidalObj_ε, monToLaxMonoidalObj_μ, monToLaxMonoidal_laxMonoidalToMon_obj_mul, monToLaxMonoidal_laxMonoidalToMon_obj_one, monToLaxMonoidal_map_hom_app, monToLaxMonoidal_obj, unitIso_hom_app_hom_app, unitIso_inv_app_hom_app, ext, ext', ext'_iff, ext_iff, isMonHom_hom, associator_hom_hom, associator_inv_hom, braiding_hom_hom, braiding_inv_hom, comp_hom, comp_hom', comp_hom'_assoc, equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, equivLaxMonoidalFunctorPUnit_functor_map_hom, equivLaxMonoidalFunctorPUnit_functor_obj_X, equivLaxMonoidalFunctorPUnit_functor_obj_mon_mul, equivLaxMonoidalFunctorPUnit_functor_obj_mon_one, equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, equivLaxMonoidalFunctorPUnit_inverse_obj_map, equivLaxMonoidalFunctorPUnit_inverse_obj_obj, equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, forget_faithful, forget_map, forget_obj, forget_δ, forget_ε, forget_η, forget_μ, hom_injective, id_hom, id_hom', instHasInitial, instIsIsoHom, instIsIsoHomOfMapForget, instIsMonHomHom, instReflectsIsomorphismsForget, leftUnitor_hom_hom, leftUnitor_inv_hom, mkIso'_hom_hom, mkIso'_inv_hom, mkIso_hom_hom, mkIso_inv_hom, monMonoidalStruct_tensorHom_hom, monMonoidalStruct_tensorObj_X, mul_def, one_def, rightUnitor_hom_hom, rightUnitor_inv_hom, tensorObj_mul, tensorObj_one, tensorUnit_X, tensorUnit_mul, tensorUnit_one, tensor_mul, tensor_one, trivial_X, trivial_mon_mul, trivial_mon_one, uniqueHomFromTrivial_default_hom, whiskerLeft_hom, whiskerRight_hom, Mon_tensor_mul_assoc, Mon_tensor_mul_one, Mon_tensor_one_mul, ext, ext_iff, instIsMonHomHomAssociator, instIsMonHomHomBraiding, instIsMonHomHomLeftUnitor, instIsMonHomHomRightUnitor, instIsMonHomId, instIsMonHomTensorHom, instIsMonHomWhiskerLeft, instIsMonHomWhiskerRight, mul_assoc, mul_assoc_assoc, mul_assoc_flip, mul_assoc_flip_assoc, mul_associator, mul_braiding, mul_def, mul_leftUnitor, mul_mul_mul_comm, mul_mul_mul_comm', mul_mul_mul_comm'_assoc, mul_mul_mul_comm_assoc, mul_one, mul_one_assoc, mul_one_hom, mul_one_hom_assoc, mul_rightUnitor, ofIso_mul, ofIso_one, one_associator, one_braiding, one_def, one_leftUnitor, one_mul, one_mul_assoc, one_mul_hom, one_mul_hom_assoc, one_rightUnitor, mul_def, one_def, instIsAddMonHomComp, instIsAddMonHomHomAsIso, instIsAddMonHomId, instIsAddMonHomNegOfHom, instIsCommAddMonObjTensorObj, instIsCommMonObjTensorObj, instIsMonHomComp, instIsMonHomHomAsIso, instIsMonHomId, instIsMonHomInvOfHom, isAddMonHom_ofIso, isMonHom_ofIso
381
Total491

CategoryTheory

Definitions

NameCategoryTheorems
AddMon 📖CompData
107 mathmath: AddMon.instIsCommAddMonObj, AddMon.whiskerLeft_hom, AddMon.equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, AddMon.equivLaxMonoidalFunctorPUnit_inverse_obj_obj, AddMon.EquivLaxMonoidalFunctorPUnit.addUnitIso_inv_app_hom_app, Equivalence.mapAddMon_inverse, AddMon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, instHasZeroObjectAddMon, AddMon.lift_hom, AddMon.EquivLaxMonoidalFunctorPUnit.addUnitIso_hom_app_hom_app, AddMon.Hom.hom_add, yonedaAddMon_obj, Equivalence.mapAddMon_functor, AddMon.forget_obj, AddMon.forget_ε, AddMon.tensorObj_add, instFullMonFunctorOppositeMonCatyonedaAddMon, Functor.mapAddMon_obj_X, AddMon.instHasInitial, AddMon.snd_hom, Functor.comp_mapAddMon_zero, AddMon.tensorAddUnit_add, AddMon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, AddMon.whiskerRight_hom, AddMon.forget_η, Functor.mapAddMonFunctor_map_app_hom, AddMon.comp_hom'_assoc, AddMon.forget_δ, AddMon.monMonoidalStruct_tensorHom_hom, Functor.essImage_mapAddMon, Functor.mapAddMonCompIso_inv_app_hom, Hom.addEquivCongrRight_symm_apply, AddMon.instReflectsIsomorphismsForget, AddMon.equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero, AddMon.comp_hom', Functor.id_mapAddMon_zero, AddMon.EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_zero, AddMon.braiding_neg_hom, AddMon.mkIso'_inv_hom, AddMon.tensor_zero, Functor.mapAddMon_map_hom, Functor.mapAddMonIdIso_hom_app_hom, AddMon.tensorAddUnit_X, AddMon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, Adjunction.mapAddMon_counit, AddMon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_obj, Functor.comp_mapAddMon_add, AddMon.hom_zero, AddMon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, AddMon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, AddMon.equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add, instFaithfulMonFunctorOppositeMonCatyonedaAddMon, AddMon.equivLaxMonoidalFunctorPUnit_functor_obj_X, AddMon.mkIso_hom_hom, AddMon.hom_add, Hom.addEquivCongrRight_apply, Functor.Full.mapAddMon, AddMon.Hom.hom_zero, AddMon.forget_faithful, Equivalence.mapAddMon_counitIso, Functor.mapAddMonNatIso_hom_app_hom, AddMon.uniqueHomFromTrivial_default_hom, Functor.mapAddMonNatTrans_app_hom, AddMon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, AddMon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, AddMon.associator_hom_hom, AddMon.monMonoidalStruct_tensorObj_X, Functor.mapAddMonFunctor_obj, AddMon.EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_add, Functor.mapAddMonNatIso_inv_app_hom, AddMon.EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_obj, AddMon.equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, essImage_yonedaAddMon, AddMon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, Functor.FullyFaithful.mapAddMon_preimage_hom, AddMon.tensorObj_zero, AddMon.EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_map_hom_app, AddMon.mkIso_inv_hom, AddMon.equivLaxMonoidalFunctorPUnit_functor_map_hom, AddMon.braiding_hom_hom, AddMon.uniqueHomToTrivial_default_hom, AddMon.rightUnitor_neg_hom, AddMon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_map, Functor.mapAddMonCompIso_hom_app_hom, AddMon.associator_neg_hom, AddMon.forget_map, AddMon.tensor_add, AddMon.leftUnitor_neg_hom, AddMon.equivLaxMonoidalFunctorPUnit_inverse_obj_map, Functor.id_mapAddMon_add, AddMon.Hom.hom_nsmul, AddMon.forget_μ, Adjunction.mapAddMon_unit, AddMon.rightUnitor_hom_hom, AddMon.mkIso'_hom_hom, AddMon.EquivLaxMonoidalFunctorPUnit.isAddMonHom_counitIsoAux, AddMon.equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, AddMon.fst_hom, Equivalence.mapAddMon_unitIso, Functor.Faithful.mapAddMon, Functor.mapAddMon_obj_addMon_zero, AddMon.id_hom', Functor.mapAddMonIdIso_inv_app_hom, AddMon.tensorAddUnit_zero, Functor.mapAddMon_obj_addMon_add, yonedaAddMon_map_app, AddMon.leftUnitor_hom_hom
AddMonObj 📖CompData
IsAddMonHom 📖CompData
26 mathmath: Functor.instIsAddMonHomμ, AddMonObj.instIsAddMonHomTensorHom, AddMonObj.instIsAddMonHomZero, AddMon.instIsAddMonHomHom, instIsAddMonHomHomAsIso, AddMonObj.instIsAddMonHomHomBraiding, AddMonObj.instIsAddMonHomAddOfIsCommAddMonObj, AddMonObj.instIsAddMonHomFst, AddMonObj.instIsAddMonHomWhiskerRight, Functor.FullyFaithful.isAddMonHom_preimage, AddMonObj.instIsAddMonHomId, AddMonObj.instIsAddMonHomHomLeftUnitor, AddMonObj.instIsAddMonHomWhiskerLeft, Functor.map.instIsAddMonHom, AddMonObj.instIsAddMonHomLift, instIsAddMonHomId, instIsAddMonHomNegOfHom, AddMonObj.instIsAddMonHomToAddUnit, AddMon.Hom.isAddMonHom_hom, AddMonObj.instIsAddMonHomHomRightUnitor, Functor.instIsAddMonHomε, AddMon.EquivLaxMonoidalFunctorPUnit.isAddMonHom_counitIsoAux, AddMonObj.instIsAddMonHomHomAssociator, instIsAddMonHomComp, AddMonObj.instIsAddMonHomSnd, isAddMonHom_ofIso
IsCommAddMonObj 📖CompData
4 mathmath: AddMon.instIsCommAddMonObj, instIsCommAddMonObjTensorObj, isCommAddMonObj_iff_isAddCommutative, IsCommAddMonObj.instTensorAddUnit
IsCommMonObj 📖CompData
18 mathmath: AlgebraicGeometry.isCommMonObj_of_isProper_of_geometricallyIntegral, CommGrp.comm, IsCommMonObj.instTensorUnit, Over.isCommMonObj_mk_pullbackSnd, Preadditive.instIsCommMonObj, IsCommMonObj.ofRepresentableBy, isCommMonObj_iff_commutator_eq_toUnit_η, AlgebraicGeometry.Scheme.isCommMonObj_asOver_pullback, Functor.isCommMonObj_obj, isCommMonObj_iff_isMulCommutative, Mon.instIsCommMonObj, instIsCommMonObjOppositeCommAlgCatXUnopMonObjCommBialgCatFunctorCommBialgCatEquivComonCommAlgCatOfIsCocommCarrier, CommGrpObj.toIsCommMonObj, Grp.instIsCommMonObj, instIsCommMonObjTensorObj, CommMon.comm, instIsCommMonObjOppositeCommAlgCatOpOfOfIsCocomm, AlgebraicGeometry.isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosed
IsMonHom 📖CompData
37 mathmath: MonObj.instIsMonHomHomAssociator, Mon.EquivLaxMonoidalFunctorPUnit.isMonHom_counitIsoAux, MonObj.instIsMonHomHomBraiding, instIsMonHomHomAsIso, Mon.instIsMonHomHom, MonObj.instIsMonHomOne, MonObj.instIsMonHomToUnit, MonObj.instIsMonHomTensorHom, Bimon.instIsMonHomComonHomEquivMonComonCounitIsoAppX, MonObj.instIsMonHomId, MonObj.mop_isMonHom, Functor.instIsMonHomμ, instIsMonHomComp, MonObj.instIsMonHomSnd, Grp.instIsMonHom, AlgebraicGeometry.Scheme.isMonHom_fst_id_right, Functor.map.instIsMonHom, MonObj.instIsMonHomHomLeftUnitor, MonObj.instIsMonHomLift, MonObj.instIsMonHomFst, instIsMonHomOppositeCommAlgCatOpOfHomToAlgHomBialgHom, isMonHom_ofIso, instIsMonHomInvOfIsCommMonObj, Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux, instIsMonHomInvHomOfIsCommMonObj, IsBimonHom.toIsMonHom, MonObj.instIsMonHomHomRightUnitor, Functor.instIsMonHomε, instIsMonHomId, Functor.FullyFaithful.isMonHom_preimage, MonObj.instIsMonHomWhiskerLeft, instIsMonHomInvOfHom, MonObj.instIsMonHomWhiskerRight, Mon.Hom.isMonHom_hom, Over.isMonHom_pullbackFst_id_right, MonObj.instIsMonHomMulOfIsCommMonObj, MonObj.unmop_isMonHom
Mon 📖CompData
395 mathmath: Grp.mkIso_inv_hom, Grp.Hom.hom_div, Grp.comp', Monoidal.MonFunctorCategoryEquivalence.inverse_obj, Grp.mkIso_hom_hom, Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, Grp.instIsIsoHomHomMon, Grp.homMk'_hom, Bimon.toMonComonObj_mon_mul_hom, Functor.mapMonNatTrans_app_hom, Bimon.equivMonComonUnitIsoAppX_hom_hom, Functor.FullyFaithful.mapMon_preimage_hom, CommMon.comp_hom, Grp.Hom.hom_hom_zpow, Equivalence.mapMon_inverse, Mon.EquivLaxMonoidalFunctorPUnit.isMonHom_counitIsoAux, Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, Functor.mapCommMonNatIso_inv_app_hom_hom, Mon.forget_obj, instFullMonFunctorOppositeMonCatYonedaMon, Mon.forgetMapConeLimitConeIso_inv_hom, Mon.leftUnitor_inv_hom, Functor.mapCommMon_obj_mon_mul, Mon.forget_μ, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, Mon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, Adjunction.mapMon_unit, Grp.id', Bimon.ext_iff, Comon.MonOpOpToComon_obj, CommMon.forget_map, Functor.FullyFaithful.mapGrp_preimage, Comon.ComonToMonOpOp_obj, Functor.mapMon_obj_mon_mul, CommGrp.mkIso_inv_hom, Mon.forget_ε, Mon.forgetMapConeLimitConeIso_hom_hom, shrinkYonedaMonObjObjEquiv_symm_comp, Bimon.toMonComon_ofMonComon_obj_one, Grp.whiskerLeft_hom_hom, Functor.mapGrpIdIso_hom_app_hom_hom, Bimon.toMon_forget, Comon.Comon_EquivMon_OpOp_counitIso, MonObj.mopEquivCompForgetIso_hom_app_unmop, Bimon.equivMonComonUnitIsoAppXAux_hom, Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, instHasZeroObjectMon, Grp.leftUnitor_hom_hom, Functor.mapCommMonNatTrans_app_hom_hom, Comon.monoidal_rightUnitor_inv_hom, Monad.monadMonEquiv_counitIso_hom_app_hom, Bimon.trivial_comon_counit_hom, Bimon.toTrivial_hom, Bimon.instIsMonHomComonHomEquivMonComonCounitIsoAppX, Bimon.instIsComonHomHomEquivMonComonCounitIsoAppXAux, Bimon.equivMonComonUnitIsoApp_hom_hom_hom, Mon.rightUnitor_inv_hom, CommMon.mkIso'_inv_hom_hom, Grp.ε_def, Grp.rightUnitor_hom_hom_hom, Bimon.toComon_obj_comon_counit, Mon.mkIso_hom_hom, Bimon.toComon_map_hom, Grp.lift_hom, Grp.hom_mul, Bimon.trivial_X_X, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, Bimon.ofMonComonObj_comon_comul_hom, Monad.monadToMon_obj, Mon.equivLaxMonoidalFunctorPUnit_functor_obj_X, Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_map_hom_app, Functor.mapMonCompIso_hom_app_hom, Mon.limitConeIsLimit_lift_hom, shrinkYonedaMon_map, Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, Grp.Hom.hom_zpow, Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, Comon.Comon_EquivMon_OpOp_functor, Grp.ofHom_hom_hom, Bimon.toComon_obj_X, Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, Mon.equivLaxMonoidalFunctorPUnit_functor_obj_mon_mul, Bimon.trivial_comon_comul_hom, Comon.MonOpOpToComon_map_hom, Grp.associator_inv_hom_hom, Monad.monToMonad_obj, Functor.mapCommMonNatIso_hom_app_hom_hom, MonObj.mopEquiv_functor_obj_mon_one_unmop, Grp.Hom.hom_hom_div, Grp.leftUnitor_hom_hom_hom, CommGrp.instIsIsoMonHomGrp, Grp.forget_map, Monoidal.monFunctorCategoryEquivalence_unitIso, Mon.tensorObj_one, Mon.lift_hom, Mon.whiskerRight_hom, Grp.mkIso_hom_hom_hom, CommMon.instIsIsoHomHomMon, Bimon.equivMonComonCounitIsoAppXAux_inv, CommGrp.forget₂CommMon_map_hom, essImage_yonedaMon, Comon.ComonToMonOpOp_map, Mon.forget_faithful, Grp.rightUnitor_inv_hom_hom, Grp.forget₂Mon_map_hom, Comon.monoidal_whiskerLeft_hom, Equivalence.mapMon_unitIso, Monoidal.monFunctorCategoryEquivalence_functor, Mon.tensorUnit_X, instFaithfulMonFunctorOppositeMonCatYonedaMon, Mon.limit_mon_mul, Functor.mapMon_obj_X, Grp.whiskerRight_hom_hom, commBialgCatEquivComonCommAlgCat_functor_obj_unop_X, Functor.mapMonNatIso_hom_app_hom, Grp.Hom.hom_hom_inv, Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, Comon.monoidal_leftUnitor_hom_hom, Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, Mon.fst_hom, CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, Grp.μ_def, Functor.mapMonNatIso_inv_app_hom, Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, Grp.snd_hom, Monoidal.MonFunctorCategoryEquivalence.functor_obj, Monad.monadToMon_map_hom, Mon.mkIso_inv_hom, Grp.whiskerLeft_hom, Bimon.equivMonComonUnitIsoAppX_inv_hom, Adjunction.mapMon_counit, shrinkYonedaMon_obj, Mon.equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, Functor.mapMonFunctor_obj, Functor.mapGrpNatIso_hom_app_hom_hom, Bimon.instIsComonHomMonHomEquivMonComonUnitIsoAppX, Functor.mapCommMonCompIso_inv_app_hom_hom, Functor.comp_mapMon_mul, Functor.mapCommMonIdIso_hom_app_hom_hom, Grp.leftUnitor_inv_hom_hom, yonedaMon_map_app, Mon.instReflectsIsomorphismsForget, Mon.associator_hom_hom, ModuleCat.MonModuleEquivalenceAlgebra.functor_map_hom_apply, Functor.mapCommGrpNatIso_inv_app_hom_hom_hom, MonObj.mopEquiv_inverse_map_hom, Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, Mon.comp_hom'_assoc, Bimon.BimonObjAux_counit, Grp.rightUnitor_inv_hom, ModuleCat.MonModuleEquivalenceAlgebra.functor_obj_carrier, Functor.mapMonFunctor_map_app_hom, Functor.mapMon_obj_mon_one, shrinkYonedaMon_map_app_shrinkYonedaObjObjEquiv_symm, Functor.mapMonIdIso_hom_app_hom, Comon.monoidal_whiskerRight_hom, Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_map_hom_hom, Monoidal.MonFunctorCategoryEquivalence.functor_map_app_hom, CommGrp.hom_ext_iff, Grp.forget₂Mon_obj_mul, Mon.equivLaxMonoidalFunctorPUnit_functor_map_hom, MonObj.mopEquiv_inverse_obj_X, Mon.tensorObj_mul, Monoidal.MonFunctorCategoryEquivalence.inverse_map_hom_app, Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, Grp.Hom.hom_pow, Grp.δ_def, Bimon.ofMonComon_toMonComon_obj_counit, Mon.whiskerLeft_hom, Grp.associator_hom_hom_hom, CommMon.mkIso_inv_hom_hom, Mon.limitCone_π_app_hom, Grp.braiding_inv_hom, Grp.mkIso'_hom_hom_hom, Grp.id_hom, Comon.monoidal_associator_hom_hom, Hom.mulEquivCongrRight_symm_apply, Functor.mapGrpCompIso_hom_app_hom_hom, Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_obj, Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, Grp.fst_hom, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, instSmallCarrierObjOppositeMonCatMonFunctorYonedaMon, Bimon.equivMonComonUnitIsoAppXAux_inv, CommGrp.mkIso_inv_hom_hom_hom, CommGrp.mkIso'_inv_hom_hom_hom, Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_mon, Mon.instIsCommMonObj, Mon.Hom.hom_mul, Monoidal.MonFunctorCategoryEquivalence.inverseObj_X, Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux, Mon.associator_inv_hom, CommMon.forget₂Mon_obj_mul, Bimon.equivMonComonCounitIsoAppX_hom_hom, Monad.monToMonad_map_toNatTrans, Mon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, Mon.equivLaxMonoidalFunctorPUnit_inverse_obj_map, Mon.mkIso'_inv_hom, Mon.uniqueHomFromTrivial_default_hom, Comon.Comon_EquivMon_OpOp_unitIso, Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, MonObj.mopEquiv_functor_map_hom_unmop, Monoidal.MonFunctorCategoryEquivalence.functorObj_map_hom, MonObj.mopEquivCompForgetIso_inv_app_unmop, Functor.mapCommMon_map_hom_hom, Functor.FullyFaithful.mapCommMon_preimage, Bimon.equivMonComonUnitIsoApp_inv_hom_hom, Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, Functor.mapGrp_map_hom_hom, CommGrp.forget₂Grp_map_hom, Grp.comp_hom_hom, Bimon.id_hom', Functor.mapMonIdIso_inv_app_hom, instIsCommMonObjOppositeCommAlgCatXUnopMonObjCommBialgCatFunctorCommBialgCatEquivComonCommAlgCatOfIsCocommCarrier, Bimon.trivialTo_hom, Equivalence.mapMon_counitIso, Bimon.ofMonComonObj_comon_counit_hom, MonObj.mopEquiv_unitIso_hom_app_hom, Grp.braiding_inv_hom_hom, Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, CommGrp.mkIso_hom_hom, Mon.instHasLimitsOfShape, Functor.mapCommMon_obj_mon_one, Bimon.ofMonComon_map_hom, Functor.Full.mapMon, Mon.tensorUnit_one, MonObj.mopEquiv_functor_obj_X_unmop, Grp.Hom.hom_mul, Mon.Hom.hom_pow, Grp.rightUnitor_hom_hom, Monad.monadMonEquiv_inverse, Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, Bimon.ofMonComon_obj, Grp.forget₂Mon_obj_X, Grp.hom_ext_iff, instPreservesLimitsOfShapeMonFunctorOppositeMonCatShrinkYonedaMon, Grp.homMk''_hom_hom, Mon.equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, Comon.monoidal_tensorUnit_comon_comul, Mon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, CommMon.id_hom, Grp.forget₂Mon_comp_forget, Bimon.toMonComon_obj, Functor.mapMon_map_hom, Functor.FullyFaithful.mapCommGrp_preimage, Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_map, Mon.leftUnitor_hom_hom, Bimon.equivMonComonCounitIsoAppX_inv_hom, Functor.mapGrpIdIso_inv_app_hom_hom, Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, Bimon.toMonComonObj_mon_one_hom, Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_map, Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_mul, CommGrp.mkIso_hom_hom_hom_hom, CommMon.homMk_hom, Grp.leftUnitor_inv_hom, Functor.id_mapMon_mul, CommMon.mkIso_hom_hom_hom, Equivalence.mapMon_functor, Bimon.toMonComon_ofMonComon_obj_mul, Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, MonObj.mopEquiv_functor_obj_mon_mul_unmop, Mon.equivLaxMonoidalFunctorPUnit_inverse_obj_obj, Bimon.BimonObjAux_comul, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isAddCommGroup, Functor.mapMonCompIso_inv_app_hom, Mon.limit_X, CommMon.hom_ext_iff, Grp.mkIso_inv_hom_hom, Bimon.equivMonComonCounitIsoApp_hom_hom_hom, Grp.snd_hom_hom, Functor.mapGrpNatTrans_app_hom_hom, Bimon.ofMonComon_toMonComon_obj_comul, Comon.monoidal_leftUnitor_inv_hom, Monoidal.monFunctorCategoryEquivalence_counitIso, CommMon.instFullMonForget₂Mon, Grp.hom_one, Grp.forget₂Mon_obj_one, Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, Mon.comp_hom', Grp.associator_inv_hom, Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, Mon.braiding_inv_hom, Grp.homMk_hom_hom, Comon.monoidal_rightUnitor_hom_hom, Functor.essImage_mapMon, Mon.forget_η, Monad.monadMonEquiv_counitIso_inv_app_hom, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, Bimon.mk'_X, Functor.mapGrpNatIso_inv_app_hom_hom, commBialgCatEquivComonCommAlgCat_inverse_obj, Mon.hom_mul, Mon.limitCone_pt, Functor.mapGrpCompIso_inv_app_hom_hom, Grp.Hom.hom_inv, CommMon.forget₂Mon_comp_forget, Mon.limit_mon_one, Functor.mapCommGrpNatIso_hom_app_hom_hom_hom, MonObj.mopEquiv_inverse_obj_mon_one, Grp.instFaithfulMonForget₂Mon, Monad.monadMonEquiv_functor, Mon.forget_δ, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, Mon.rightUnitor_hom_hom, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_carrier, Bimon.ofMonComonObj_X, Grp.braiding_hom_hom, Functor.mapCommGrp_map_hom_hom_hom, Grp.η_def, Comon.monoidal_associator_inv_hom, Comon.Comon_EquivMon_OpOp_inverse, Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, Bimon.toMonComon_map_hom, shrinkYonedaMon_obj_map_shrinkYonedaMonObjObjEquiv_symm, Grp.associator_hom_hom, Preadditive.commGrpEquivalence_inverse_map, Mon.forget_map, Mon.equivLaxMonoidalFunctorPUnit_functor_obj_mon_one, Mon.instPreservesLimitsOfShapeForgetOfHasLimitsOfShape, Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, Functor.mapCommGrpNatTrans_app_hom_hom_hom, Functor.mapCommMonIdIso_inv_app_hom_hom, Comon.monoidal_tensorUnit_comon_counit, MonObj.mopEquiv_unitIso_inv_app_hom, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CommMon.forget₂Mon_obj_X, ModuleCat.MonModuleEquivalenceAlgebra.inverse_map_hom, Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isModule, Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_obj, yonedaGrp_map_app, Bimon.equivMonComonCounitIsoAppXAux_hom, Mon.monMonoidalStruct_tensorHom_hom, CommGrp.mkIso'_hom_hom_hom_hom, Grp.whiskerRight_hom, Mon.braiding_hom_hom, Grp.tensorHom_hom, Monoidal.MonFunctorCategoryEquivalence.functorObj_obj, Hom.mulEquivCongrRight_apply, CommMon.mkIso'_hom_hom_hom, Grp.Hom.hom_one, CommMon.instFaithfulMonForget₂Mon, Mon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, Grp.fst_hom_hom, Grp.mkIso'_inv_hom_hom, Comon.monoidal_tensorHom_hom, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, Functor.id_mapMon_one, Bimon.trivial_X_mon_mul, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, Preadditive.commGrpEquivalence_functor_map_hom_hom_hom, Bimon.comp_hom', Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, Grp.braiding_hom_hom_hom, Mon.tensorUnit_mul, Mon.uniqueHomToTrivial_default_hom, Bimon.equivMonComonCounitIsoApp_inv_hom_hom, CommMon.forget₂Mon_map_hom, Mon.tensor_one, Mon.hom_one, yonedaMon_obj, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, Mon.mkIso'_hom_hom, Mon.monMonoidalStruct_tensorObj_X, Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, Monoidal.monFunctorCategoryEquivalence_inverse, Functor.comp_mapMon_one, Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_one, Monoidal.CommMonFunctorCategoryEquivalence.functor_map_app_hom_hom, CommMon.forget₂Mon_obj_one, Grp.comp_hom, Mon.id_hom', Grp.instFullMonForget₂Mon, Grp.id_hom_hom, shrinkYonedaGrp_map_app_shrinkYonedaObjObjEquiv_symm, Functor.Faithful.mapMon, Bimon.toComon_obj_comon_comul, Mon.snd_hom, Mon.equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, Mon.Hom.hom_one, CommGrp.forget_map, Mon.instHasInitial, Comon.monoidal_tensorObj_comon_comul, Bimon.trivial_X_mon_one, Mon.tensor_mul, Functor.mapCommMonCompIso_hom_app_hom_hom, MonObj.mopEquiv_inverse_obj_mon_mul
MonObj 📖CompData
1 mathmath: GrpObj.toMonObj_injective

Theorems

NameKindAssumesProvesValidatesDepends On
instIsAddMonHomComp 📖mathematicalIsAddMonHom
CategoryStruct.comp
Category.toCategoryStruct
IsAddMonHom.zero_hom_assoc
IsAddMonHom.zero_hom
IsAddMonHom.add_hom_assoc
IsAddMonHom.add_hom
MonoidalCategory.tensorHom_comp_tensorHom_assoc
instIsAddMonHomHomAsIso 📖mathematicalIsAddMonHom
Iso.hom
asIso
instIsAddMonHomId 📖mathematicalIsAddMonHom
CategoryStruct.id
Category.toCategoryStruct
Category.comp_id
MonoidalCategory.tensorHom_id
MonoidalCategory.id_whiskerRight
Category.id_comp
instIsAddMonHomNegOfHom 📖mathematicalIsAddMonHom
Iso.inv
Iso.comp_inv_eq
IsAddMonHom.zero_hom
Category.assoc
IsAddMonHom.add_hom
MonoidalCategory.tensorHom_comp_tensorHom_assoc
Iso.inv_hom_id
MonoidalCategory.tensorHom_id
MonoidalCategory.id_whiskerRight
Category.id_comp
instIsCommAddMonObjTensorObj 📖mathematicalIsCommAddMonObj
SymmetricCategory.toBraidedCategory
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
AddMon.instAddMonObjTensorObj
Iso.isIso_hom
BraidedCategory.braiding_tensor_right_hom
BraidedCategory.braiding_tensor_left_hom
SymmetricCategory.braiding_swap_eq_inv_braiding
MonoidalCategory.comp_whiskerRight
MonoidalCategory.whisker_assoc
Category.assoc
MonoidalCategory.pentagon_inv_hom_hom_hom_inv_assoc
MonoidalCategory.whiskerLeft_comp_assoc
Iso.inv_hom_id_assoc
Iso.hom_inv_id_assoc
MonoidalCategory.hom_inv_whiskerRight_assoc
Iso.inv_hom_id
Category.comp_id
IsIso.inv_comp_eq
MonoidalCategory.whiskerLeft_isIso
IsIso.comp_isIso
Iso.isIso_inv
MonoidalCategory.whiskerRight_isIso
IsIso.Iso.inv_hom
MonoidalCategory.inv_whiskerLeft
IsIso.inv_comp
MonoidalCategory.inv_whiskerRight
IsIso.Iso.inv_inv
MonoidalCategory.hom_inv_whiskerRight
MonoidalCategory.pentagon_inv_assoc
MonoidalCategory.associator_inv_naturality_left_assoc
MonoidalCategory.associator_naturality_right_assoc
MonoidalCategory.tensorHom_def_assoc
MonoidalCategory.tensorHom_comp_tensorHom
IsCommAddMonObj.add_comm
instIsCommMonObjTensorObj 📖mathematicalIsCommMonObj
SymmetricCategory.toBraidedCategory
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
Mon.instMonObjTensorObj
Iso.isIso_hom
BraidedCategory.braiding_tensor_right_hom
BraidedCategory.braiding_tensor_left_hom
SymmetricCategory.braiding_swap_eq_inv_braiding
MonoidalCategory.comp_whiskerRight
MonoidalCategory.whisker_assoc
Category.assoc
MonoidalCategory.pentagon_inv_hom_hom_hom_inv_assoc
Iso.inv_hom_id_assoc
Iso.hom_inv_id_assoc
MonoidalCategory.hom_inv_whiskerRight_assoc
Iso.inv_hom_id
Category.comp_id
MonoidalCategory.whiskerLeft_isIso
IsIso.comp_isIso
Iso.isIso_inv
MonoidalCategory.whiskerRight_isIso
IsIso.Iso.inv_hom
MonoidalCategory.inv_whiskerLeft
IsIso.inv_comp
MonoidalCategory.inv_whiskerRight
IsIso.Iso.inv_inv
MonoidalCategory.hom_inv_whiskerRight
MonoidalCategory.pentagon_inv_assoc
MonoidalCategory.tensorHom_comp_tensorHom
IsCommMonObj.mul_comm
instIsMonHomComp 📖mathematicalIsMonHom
CategoryStruct.comp
Category.toCategoryStruct
IsMonHom.one_hom_assoc
IsMonHom.one_hom
IsMonHom.mul_hom_assoc
IsMonHom.mul_hom
MonoidalCategory.tensorHom_comp_tensorHom_assoc
instIsMonHomHomAsIso 📖mathematicalIsMonHom
Iso.hom
asIso
instIsMonHomId 📖mathematicalIsMonHom
CategoryStruct.id
Category.toCategoryStruct
Category.comp_id
MonoidalCategory.tensorHom_id
MonoidalCategory.id_whiskerRight
Category.id_comp
instIsMonHomInvOfHom 📖mathematicalIsMonHom
Iso.inv
IsMonHom.one_hom
Category.assoc
IsMonHom.mul_hom
MonoidalCategory.tensorHom_comp_tensorHom_assoc
Iso.inv_hom_id
MonoidalCategory.tensorHom_id
MonoidalCategory.id_whiskerRight
Category.id_comp
isAddMonHom_ofIso 📖mathematicalIsAddMonHom
AddMonObj.ofIso
Iso.hom
MonoidalCategory.tensorHom_comp_tensorHom_assoc
Iso.hom_inv_id
MonoidalCategory.tensorHom_id
MonoidalCategory.id_whiskerRight
Category.id_comp
isMonHom_ofIso 📖mathematicalIsMonHom
MonObj.ofIso
Iso.hom
MonoidalCategory.tensorHom_comp_tensorHom_assoc
Iso.hom_inv_id
MonoidalCategory.tensorHom_id
MonoidalCategory.id_whiskerRight
Category.id_comp

CategoryTheory.AddMon

Definitions

NameCategoryTheorems
X 📖CompOp
87 mathmath: whiskerLeft_hom, hom_injective, equivLaxMonoidalFunctorPUnit_inverse_obj_obj, EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, lift_hom, Hom.hom_add, CategoryTheory.yonedaAddMon_obj, forget_obj, tensorObj_add, comp_hom, CategoryTheory.Functor.mapAddMon_obj_X, snd_hom, CategoryTheory.Functor.comp_mapAddMon_zero, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj_obj, tensorAddUnit_add, equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, whiskerRight_hom, CategoryTheory.Functor.mapAddMonFunctor_map_app_hom, comp_hom'_assoc, id_hom, forget_δ, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj_μ, instIsAddMonHomHom, monMonoidalStruct_tensorHom_hom, CategoryTheory.Functor.essImage_mapAddMon, CategoryTheory.Functor.mapAddMonCompIso_inv_app_hom, CategoryTheory.Hom.addEquivCongrRight_symm_apply, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero, comp_hom', CategoryTheory.Functor.id_mapAddMon_zero, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_zero, braiding_neg_hom, tensor_zero, CategoryTheory.Functor.mapAddMon_map_hom, CategoryTheory.Functor.mapAddMonIdIso_hom_app_hom, tensorAddUnit_X, EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj_map, CategoryTheory.Functor.comp_mapAddMon_add, hom_zero, EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add, equivLaxMonoidalFunctorPUnit_functor_obj_X, mkIso_hom_hom, hom_add, CategoryTheory.Hom.addEquivCongrRight_apply, Hom.hom_zero, CategoryTheory.Functor.mapAddMonNatIso_hom_app_hom, uniqueHomFromTrivial_default_hom, CategoryTheory.Functor.mapAddMonNatTrans_app_hom, equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, associator_hom_hom, monMonoidalStruct_tensorObj_X, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_add, CategoryTheory.Functor.mapAddMonNatIso_inv_app_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, CategoryTheory.Functor.FullyFaithful.mapAddMon_preimage_hom, Hom.isAddMonHom_hom, tensorObj_zero, mkIso_inv_hom, braiding_hom_hom, uniqueHomToTrivial_default_hom, rightUnitor_neg_hom, CategoryTheory.Functor.mapAddMonCompIso_hom_app_hom, instIsIsoHom, associator_neg_hom, tensor_add, leftUnitor_neg_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_map, CategoryTheory.Functor.id_mapAddMon_add, Hom.hom_nsmul, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj_ε, trivial_X, forget_μ, rightUnitor_hom_hom, EquivLaxMonoidalFunctorPUnit.isAddMonHom_counitIsoAux, instIsIsoHomOfMapForget, fst_hom, CategoryTheory.Functor.mapAddMon_obj_addMon_zero, id_hom', CategoryTheory.Functor.mapAddMonIdIso_inv_app_hom, tensorAddUnit_zero, CategoryTheory.Functor.mapAddMon_obj_addMon_add, CategoryTheory.yonedaAddMon_map_app, leftUnitor_hom_hom
addMon 📖CompOp
41 mathmath: add_def, trivial_addMon_zero, Hom.hom_add, CategoryTheory.yonedaAddMon_obj, tensorObj_add, CategoryTheory.Functor.comp_mapAddMon_zero, tensorAddUnit_add, trivial_addMon_add, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj_μ, instIsAddMonHomHom, monMonoidalStruct_tensorHom_hom, CategoryTheory.Hom.addEquivCongrRight_symm_apply, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero, CategoryTheory.Functor.id_mapAddMon_zero, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_zero, tensor_zero, CategoryTheory.Functor.mapAddMon_map_hom, CategoryTheory.Functor.comp_mapAddMon_add, hom_zero, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add, mkIso_hom_hom, hom_add, CategoryTheory.Hom.addEquivCongrRight_apply, Hom.hom_zero, uniqueHomFromTrivial_default_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_add, zero_def, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, Hom.isAddMonHom_hom, tensorObj_zero, mkIso_inv_hom, tensor_add, CategoryTheory.Functor.id_mapAddMon_add, Hom.hom_nsmul, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj_ε, EquivLaxMonoidalFunctorPUnit.isAddMonHom_counitIsoAux, CategoryTheory.Functor.mapAddMon_obj_addMon_zero, tensorAddUnit_zero, CategoryTheory.Functor.mapAddMon_obj_addMon_add, CategoryTheory.yonedaAddMon_map_app
comp 📖CompOp
1 mathmath: comp_hom
equivLaxMonoidalFunctorPUnit 📖CompOp
13 mathmath: equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, equivLaxMonoidalFunctorPUnit_inverse_obj_obj, equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add, equivLaxMonoidalFunctorPUnit_functor_obj_X, equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, equivLaxMonoidalFunctorPUnit_functor_map_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_map, equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app
forget 📖CompOp
8 mathmath: forget_obj, forget_ε, forget_η, forget_δ, instReflectsIsomorphismsForget, forget_faithful, forget_map, forget_μ
homInhabited 📖CompOp
id 📖CompOp
1 mathmath: id_hom
instAddMonObjTensorObj 📖CompOp
10 mathmath: add_def, CategoryTheory.Functor.instIsAddMonHomμ, CategoryTheory.instIsCommAddMonObjTensorObj, CategoryTheory.AddMonObj.instIsAddMonHomHomBraiding, CategoryTheory.AddMonObj.add_braiding, CategoryTheory.AddMonObj.instIsAddMonHomAddOfIsCommAddMonObj, CategoryTheory.AddMonObj.instIsAddMonHomFst, CategoryTheory.AddMonObj.instIsAddMonHomLift, zero_def, CategoryTheory.AddMonObj.instIsAddMonHomSnd
instCategory 📖CompOp
107 mathmath: instIsCommAddMonObj, whiskerLeft_hom, equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, equivLaxMonoidalFunctorPUnit_inverse_obj_obj, EquivLaxMonoidalFunctorPUnit.addUnitIso_inv_app_hom_app, CategoryTheory.Equivalence.mapAddMon_inverse, EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, CategoryTheory.instHasZeroObjectAddMon, lift_hom, EquivLaxMonoidalFunctorPUnit.addUnitIso_hom_app_hom_app, Hom.hom_add, CategoryTheory.yonedaAddMon_obj, CategoryTheory.Equivalence.mapAddMon_functor, forget_obj, forget_ε, tensorObj_add, CategoryTheory.instFullMonFunctorOppositeMonCatyonedaAddMon, CategoryTheory.Functor.mapAddMon_obj_X, instHasInitial, snd_hom, CategoryTheory.Functor.comp_mapAddMon_zero, tensorAddUnit_add, equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, whiskerRight_hom, forget_η, CategoryTheory.Functor.mapAddMonFunctor_map_app_hom, comp_hom'_assoc, forget_δ, monMonoidalStruct_tensorHom_hom, CategoryTheory.Functor.essImage_mapAddMon, CategoryTheory.Functor.mapAddMonCompIso_inv_app_hom, CategoryTheory.Hom.addEquivCongrRight_symm_apply, instReflectsIsomorphismsForget, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero, comp_hom', CategoryTheory.Functor.id_mapAddMon_zero, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_zero, braiding_neg_hom, mkIso'_inv_hom, tensor_zero, CategoryTheory.Functor.mapAddMon_map_hom, CategoryTheory.Functor.mapAddMonIdIso_hom_app_hom, tensorAddUnit_X, EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, CategoryTheory.Adjunction.mapAddMon_counit, EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_obj, CategoryTheory.Functor.comp_mapAddMon_add, hom_zero, EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add, CategoryTheory.instFaithfulMonFunctorOppositeMonCatyonedaAddMon, equivLaxMonoidalFunctorPUnit_functor_obj_X, mkIso_hom_hom, hom_add, CategoryTheory.Hom.addEquivCongrRight_apply, CategoryTheory.Functor.Full.mapAddMon, Hom.hom_zero, forget_faithful, CategoryTheory.Equivalence.mapAddMon_counitIso, CategoryTheory.Functor.mapAddMonNatIso_hom_app_hom, uniqueHomFromTrivial_default_hom, CategoryTheory.Functor.mapAddMonNatTrans_app_hom, equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, associator_hom_hom, monMonoidalStruct_tensorObj_X, CategoryTheory.Functor.mapAddMonFunctor_obj, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_add, CategoryTheory.Functor.mapAddMonNatIso_inv_app_hom, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_obj, equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, CategoryTheory.essImage_yonedaAddMon, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, CategoryTheory.Functor.FullyFaithful.mapAddMon_preimage_hom, tensorObj_zero, EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_map_hom_app, mkIso_inv_hom, equivLaxMonoidalFunctorPUnit_functor_map_hom, braiding_hom_hom, uniqueHomToTrivial_default_hom, rightUnitor_neg_hom, EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_map, CategoryTheory.Functor.mapAddMonCompIso_hom_app_hom, associator_neg_hom, forget_map, tensor_add, leftUnitor_neg_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_map, CategoryTheory.Functor.id_mapAddMon_add, Hom.hom_nsmul, forget_μ, CategoryTheory.Adjunction.mapAddMon_unit, rightUnitor_hom_hom, mkIso'_hom_hom, EquivLaxMonoidalFunctorPUnit.isAddMonHom_counitIsoAux, equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, fst_hom, CategoryTheory.Equivalence.mapAddMon_unitIso, CategoryTheory.Functor.Faithful.mapAddMon, CategoryTheory.Functor.mapAddMon_obj_addMon_zero, id_hom', CategoryTheory.Functor.mapAddMonIdIso_inv_app_hom, tensorAddUnit_zero, CategoryTheory.Functor.mapAddMon_obj_addMon_add, CategoryTheory.yonedaAddMon_map_app, leftUnitor_hom_hom
instInhabited 📖CompOp
instMonoidalForget 📖CompOp
4 mathmath: forget_ε, forget_η, forget_δ, forget_μ
instSymmetricCategory 📖CompOp
3 mathmath: instIsCommAddMonObj, braiding_neg_hom, braiding_hom_hom
mkIso 📖CompOp
2 mathmath: mkIso_hom_hom, mkIso_inv_hom
mkIso' 📖CompOp
4 mathmath: CategoryTheory.Hom.addEquivCongrRight_symm_apply, mkIso'_inv_hom, CategoryTheory.Hom.addEquivCongrRight_apply, mkIso'_hom_hom
monMonoidal 📖CompOp
9 mathmath: instIsCommAddMonObj, forget_ε, forget_η, forget_δ, braiding_neg_hom, hom_zero, hom_add, braiding_hom_hom, forget_μ
monMonoidalStruct 📖CompOp
17 mathmath: whiskerLeft_hom, tensorObj_add, tensorAddUnit_add, whiskerRight_hom, monMonoidalStruct_tensorHom_hom, tensor_zero, tensorAddUnit_X, associator_hom_hom, monMonoidalStruct_tensorObj_X, tensorObj_zero, rightUnitor_neg_hom, associator_neg_hom, tensor_add, leftUnitor_neg_hom, rightUnitor_hom_hom, tensorAddUnit_zero, leftUnitor_hom_hom
trivial 📖CompOp
10 mathmath: trivial_addMon_zero, trivial_addMon_add, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero, EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_obj, equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add, uniqueHomFromTrivial_default_hom, equivLaxMonoidalFunctorPUnit_functor_map_hom, uniqueHomToTrivial_default_hom, EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_map, trivial_X
uniqueHomFromTrivial 📖CompOp
1 mathmath: uniqueHomFromTrivial_default_hom

Theorems

NameKindAssumesProvesValidatesDepends On
add_def 📖mathematicalCategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instAddMonObjTensorObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
addMon
associator_hom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
associator_neg_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
braiding_hom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
monMonoidal
CategoryTheory.SymmetricCategory.toBraidedCategory
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
instSymmetricCategory
X
braiding_neg_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
monMonoidal
CategoryTheory.SymmetricCategory.toBraidedCategory
CategoryTheory.Iso.inv
CategoryTheory.BraidedCategory.braiding
instSymmetricCategory
X
comp_hom 📖mathematicalHom.hom
comp
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
X
comp_hom' 📖mathematicalHom.hom
CategoryTheory.CategoryStruct.comp
CategoryTheory.AddMon
CategoryTheory.Category.toCategoryStruct
instCategory
X
comp_hom'_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
X
Hom.hom
CategoryTheory.AddMon
instCategory
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_hom'
equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom 📖mathematicalHom.hom
CategoryTheory.Functor.obj
CategoryTheory.AddMon
instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal
EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon
CategoryTheory.Functor.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.counitIso
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
X
equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom 📖mathematicalHom.hom
CategoryTheory.Functor.obj
CategoryTheory.AddMon
instCategory
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal
EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.counitIso
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
X
equivLaxMonoidalFunctorPUnit_functor_map_hom 📖mathematicalHom.hom
CategoryTheory.Functor.obj
CategoryTheory.AddMon
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.mapAddMonFunctor
trivial
CategoryTheory.Functor.map
CategoryTheory.Equivalence.functor
equivLaxMonoidalFunctorPUnit
CategoryTheory.NatTrans.app
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
equivLaxMonoidalFunctorPUnit_functor_obj_X 📖mathematicalX
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.AddMon
instCategory
CategoryTheory.Equivalence.functor
equivLaxMonoidalFunctorPUnit
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add 📖mathematicalCategoryTheory.AddMonObj.add
CategoryTheory.Functor.obj
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
X
trivial
addMon
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.AddMon
instCategory
CategoryTheory.Equivalence.functor
equivLaxMonoidalFunctorPUnit
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Discrete.functor_map_id
CategoryTheory.Category.comp_id
equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero 📖mathematicalCategoryTheory.AddMonObj.zero
CategoryTheory.Functor.obj
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
X
trivial
addMon
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.AddMon
instCategory
CategoryTheory.Equivalence.functor
equivLaxMonoidalFunctorPUnit
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.Discrete.functor_map_id
CategoryTheory.Category.comp_id
equivLaxMonoidalFunctorPUnit_inverse_map_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.of
EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj
EquivLaxMonoidalFunctorPUnit.instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Functor.map
CategoryTheory.AddMon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
Hom.hom
equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε 📖mathematicalCategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.Functor.obj
CategoryTheory.AddMon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
CategoryTheory.AddMonObj.zero
X
addMon
equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ 📖mathematicalCategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.Functor.obj
CategoryTheory.AddMon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
CategoryTheory.AddMonObj.add
X
addMon
equivLaxMonoidalFunctorPUnit_inverse_obj_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.AddMon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
X
equivLaxMonoidalFunctorPUnit_inverse_obj_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.AddMon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
X
equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.AddMon
instCategory
EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon
EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.unitIso
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Discrete.functor_map_id
equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor.comp
CategoryTheory.AddMon
instCategory
EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon
EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal
CategoryTheory.Functor.id
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.unitIso
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Discrete.functor_map_id
forget_faithful 📖mathematicalCategoryTheory.Functor.Faithful
CategoryTheory.AddMon
instCategory
forget
Hom.ext'
forget_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.AddMon
instCategory
forget
Hom.hom
forget_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.AddMon
instCategory
forget
X
forget_δ 📖mathematicalCategoryTheory.Functor.OplaxMonoidal.δ
CategoryTheory.AddMon
instCategory
monMonoidal
forget
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
instMonoidalForget
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
forget_ε 📖mathematicalCategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.AddMon
instCategory
monMonoidal
forget
CategoryTheory.Functor.Monoidal.toLaxMonoidal
instMonoidalForget
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
forget_η 📖mathematicalCategoryTheory.Functor.OplaxMonoidal.η
CategoryTheory.AddMon
instCategory
monMonoidal
forget
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
instMonoidalForget
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
forget_μ 📖mathematicalCategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.AddMon
instCategory
monMonoidal
forget
CategoryTheory.Functor.Monoidal.toLaxMonoidal
instMonoidalForget
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
hom_injective 📖mathematicalHom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
X
Hom.hom
Hom.ext
id_hom 📖mathematicalHom.hom
id
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
X
id_hom' 📖mathematicalHom.hom
CategoryTheory.CategoryStruct.id
CategoryTheory.AddMon
CategoryTheory.Category.toCategoryStruct
instCategory
X
instHasInitial 📖mathematicalCategoryTheory.Limits.HasInitial
CategoryTheory.AddMon
instCategory
CategoryTheory.Limits.hasInitial_of_unique
Unique.instSubsingleton
instIsAddMonHomHom 📖mathematicalCategoryTheory.IsAddMonHom
X
addMon
Hom.hom
Hom.isAddMonHom_hom
instIsIsoHom 📖mathematicalCategoryTheory.IsIso
X
Hom.hom
instIsIsoHomOfMapForget 📖mathematicalCategoryTheory.IsIso
X
Hom.hom
instReflectsIsomorphismsForget 📖mathematicalCategoryTheory.Functor.ReflectsIsomorphisms
CategoryTheory.AddMon
instCategory
forget
instIsIsoHomOfMapForget
CategoryTheory.IsIso.comp_inv_eq
CategoryTheory.IsAddMonHom.zero_hom
instIsAddMonHomHom
CategoryTheory.Category.assoc
CategoryTheory.IsAddMonHom.add_hom
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc
CategoryTheory.IsIso.inv_hom_id
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.Category.id_comp
Hom.ext'
CategoryTheory.IsIso.hom_inv_id
leftUnitor_hom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
leftUnitor_neg_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
mkIso'_hom_hom 📖mathematicalHom.hom
CategoryTheory.Iso.hom
CategoryTheory.AddMon
instCategory
mkIso'
mkIso'_inv_hom 📖mathematicalHom.hom
CategoryTheory.Iso.inv
CategoryTheory.AddMon
instCategory
mkIso'
mkIso_hom_hom 📖mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
CategoryTheory.CategoryStruct.comp
CategoryTheory.AddMonObj.zero
addMon
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategoryStruct.tensorHom
Hom.hom
X
addMon
CategoryTheory.Iso.hom
CategoryTheory.AddMon
instCategory
mkIso
mkIso_inv_hom 📖mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
CategoryTheory.CategoryStruct.comp
CategoryTheory.AddMonObj.zero
addMon
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategoryStruct.tensorHom
Hom.hom
X
addMon
CategoryTheory.Iso.inv
CategoryTheory.AddMon
instCategory
mkIso
monMonoidalStruct_tensorHom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
CategoryTheory.AddMonObj.tensorObj.instTensorObj
addMon
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMon
instCategory
monMonoidalStruct
monMonoidalStruct_tensorObj_X 📖mathematicalX
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
rightUnitor_hom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
rightUnitor_neg_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
tensorAddUnit_X 📖mathematicalX
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorAddUnit_add 📖mathematicalCategoryTheory.AddMonObj.add
X
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.AddMon
instCategory
monMonoidalStruct
addMon
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.leftUnitor
tensorAddUnit_zero 📖mathematicalCategoryTheory.AddMonObj.zero
X
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.AddMon
instCategory
monMonoidalStruct
addMon
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorObj_add 📖mathematicalCategoryTheory.AddMonObj.add
X
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensorObj_zero 📖mathematicalCategoryTheory.AddMonObj.zero
X
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensor_add 📖mathematicalCategoryTheory.AddMonObj.add
X
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensor_zero 📖mathematicalCategoryTheory.AddMonObj.zero
X
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
trivial_X 📖mathematicalX
trivial
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
trivial_addMon_add 📖mathematicalCategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
addMon
trivial
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategoryStruct.leftUnitor
trivial_addMon_zero 📖mathematicalCategoryTheory.AddMonObj.zero
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
addMon
trivial
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
uniqueHomFromTrivial_default_hom 📖mathematicalHom.hom
trivial
Quiver.Hom
CategoryTheory.AddMon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
instCategory
Unique.toInhabited
uniqueHomFromTrivial
CategoryTheory.AddMonObj.zero
X
addMon
whiskerLeft_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
whiskerRight_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
zero_def 📖mathematicalCategoryTheory.AddMonObj.zero
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instAddMonObjTensorObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
addMon

CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit

Definitions

NameCategoryTheorems
addMonToLaxMonoidal 📖CompOp
15 mathmath: addUnitIso_inv_app_hom_app, counitIso_inv_app_hom, addUnitIso_hom_app_hom_app, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, addMonToLaxMonoidal_laxMonoidalToAddMon_obj_zero, counitIsoAux_hom, counitIso_hom_app_hom, counitIsoAux_inv, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, addMonToLaxMonoidal_laxMonoidalToAddMon_obj_add, addMonToLaxMonoidal_obj, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, addMonToLaxMonoidal_map_hom_app, isAddMonHom_counitIsoAux, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app
addMonToLaxMonoidalObj 📖CompOp
9 mathmath: CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, addMonToLaxMonoidalObj_obj, addMonToLaxMonoidalObj_μ, addMonToLaxMonoidalObj_map, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, addMonToLaxMonoidal_obj, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, addMonToLaxMonoidal_map_hom_app, addMonToLaxMonoidalObj_ε
addUnitIso 📖CompOp
2 mathmath: addUnitIso_inv_app_hom_app, addUnitIso_hom_app_hom_app
counitIso 📖CompOp
2 mathmath: counitIso_inv_app_hom, counitIso_hom_app_hom
counitIsoAux 📖CompOp
3 mathmath: counitIsoAux_hom, counitIsoAux_inv, isAddMonHom_counitIsoAux
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj 📖CompOp
5 mathmath: CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, addMonToLaxMonoidalObj_μ, addMonToLaxMonoidal_obj, addMonToLaxMonoidal_map_hom_app, addMonToLaxMonoidalObj_ε
laxMonoidalToAddMon 📖CompOp
15 mathmath: addUnitIso_inv_app_hom_app, counitIso_inv_app_hom, addUnitIso_hom_app_hom_app, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, addMonToLaxMonoidal_laxMonoidalToAddMon_obj_zero, counitIsoAux_hom, laxMonoidalToAddMon_obj, counitIso_hom_app_hom, counitIsoAux_inv, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, addMonToLaxMonoidal_laxMonoidalToAddMon_obj_add, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, laxMonoidalToAddMon_map, isAddMonHom_counitIsoAux, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app

Theorems

NameKindAssumesProvesValidatesDepends On
addMonToLaxMonoidalObj_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Discrete
CategoryTheory.discreteCategory
addMonToLaxMonoidalObj
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.X
addMonToLaxMonoidalObj_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Discrete
CategoryTheory.discreteCategory
addMonToLaxMonoidalObj
CategoryTheory.AddMon.X
addMonToLaxMonoidalObj_ε 📖mathematicalCategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
addMonToLaxMonoidalObj
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
CategoryTheory.AddMonObj.zero
CategoryTheory.AddMon.X
CategoryTheory.AddMon.addMon
addMonToLaxMonoidalObj_μ 📖mathematicalCategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
addMonToLaxMonoidalObj
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
CategoryTheory.AddMonObj.add
CategoryTheory.AddMon.X
CategoryTheory.AddMon.addMon
addMonToLaxMonoidal_laxMonoidalToAddMon_obj_add 📖mathematicalCategoryTheory.AddMonObj.add
CategoryTheory.AddMon.X
CategoryTheory.Functor.obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
addMonToLaxMonoidal
laxMonoidalToAddMon
CategoryTheory.AddMon.addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.id
addMonToLaxMonoidal_laxMonoidalToAddMon_obj_zero 📖mathematicalCategoryTheory.AddMonObj.zero
CategoryTheory.AddMon.X
CategoryTheory.Functor.obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
addMonToLaxMonoidal
laxMonoidalToAddMon
CategoryTheory.AddMon.addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.id
addMonToLaxMonoidal_map_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.of
addMonToLaxMonoidalObj
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Functor.map
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
addMonToLaxMonoidal
CategoryTheory.AddMon.Hom.hom
addMonToLaxMonoidal_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
addMonToLaxMonoidal
CategoryTheory.LaxMonoidalFunctor.of
addMonToLaxMonoidalObj
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
addUnitIso_hom_app_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
laxMonoidalToAddMon
addMonToLaxMonoidal
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
addUnitIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Discrete.functor_map_id
addUnitIso_inv_app_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor.comp
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
laxMonoidalToAddMon
addMonToLaxMonoidal
CategoryTheory.Functor.id
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
addUnitIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Discrete.functor_map_id
counitIsoAux_hom 📖mathematicalCategoryTheory.Iso.hom
CategoryTheory.AddMon.X
CategoryTheory.Functor.obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
addMonToLaxMonoidal
laxMonoidalToAddMon
CategoryTheory.Functor.id
counitIsoAux
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
counitIsoAux_inv 📖mathematicalCategoryTheory.Iso.inv
CategoryTheory.AddMon.X
CategoryTheory.Functor.obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
addMonToLaxMonoidal
laxMonoidalToAddMon
CategoryTheory.Functor.id
counitIsoAux
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
counitIso_hom_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
CategoryTheory.Functor.obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
addMonToLaxMonoidal
laxMonoidalToAddMon
CategoryTheory.Functor.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
counitIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.X
counitIso_inv_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
CategoryTheory.Functor.obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
addMonToLaxMonoidal
laxMonoidalToAddMon
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
counitIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.X
isAddMonHom_counitIsoAux 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.AddMon.X
CategoryTheory.Functor.obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
addMonToLaxMonoidal
laxMonoidalToAddMon
CategoryTheory.Functor.id
CategoryTheory.AddMon.addMon
CategoryTheory.Iso.hom
counitIsoAux
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.Category.id_comp
laxMonoidalToAddMon_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
laxMonoidalToAddMon
CategoryTheory.NatTrans.app
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.mapAddMonFunctor
CategoryTheory.AddMon.trivial
laxMonoidalToAddMon_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
laxMonoidalToAddMon
CategoryTheory.Functor.mapAddMon
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.AddMon.trivial

CategoryTheory.AddMon.Hom

Definitions

NameCategoryTheorems
hom 📖CompOp
56 mathmath: CategoryTheory.AddMon.whiskerLeft_hom, CategoryTheory.AddMon.hom_injective, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, CategoryTheory.AddMon.lift_hom, hom_add, CategoryTheory.AddMon.comp_hom, CategoryTheory.AddMon.snd_hom, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, CategoryTheory.AddMon.whiskerRight_hom, CategoryTheory.Functor.mapAddMonFunctor_map_app_hom, CategoryTheory.AddMon.comp_hom'_assoc, ext'_iff, CategoryTheory.AddMon.id_hom, CategoryTheory.AddMon.instIsAddMonHomHom, CategoryTheory.AddMon.monMonoidalStruct_tensorHom_hom, CategoryTheory.Functor.mapAddMonCompIso_inv_app_hom, CategoryTheory.AddMon.comp_hom', CategoryTheory.AddMon.braiding_neg_hom, CategoryTheory.AddMon.mkIso'_inv_hom, CategoryTheory.Functor.mapAddMon_map_hom, CategoryTheory.Functor.mapAddMonIdIso_hom_app_hom, CategoryTheory.AddMon.hom_zero, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, CategoryTheory.AddMon.mkIso_hom_hom, CategoryTheory.AddMon.hom_add, hom_zero, CategoryTheory.Functor.mapAddMonNatIso_hom_app_hom, CategoryTheory.AddMon.uniqueHomFromTrivial_default_hom, CategoryTheory.Functor.mapAddMonNatTrans_app_hom, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, CategoryTheory.AddMon.associator_hom_hom, CategoryTheory.Functor.mapAddMonNatIso_inv_app_hom, CategoryTheory.Functor.FullyFaithful.mapAddMon_preimage_hom, isAddMonHom_hom, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_map_hom_app, CategoryTheory.AddMon.mkIso_inv_hom, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_functor_map_hom, CategoryTheory.AddMon.braiding_hom_hom, CategoryTheory.AddMon.uniqueHomToTrivial_default_hom, CategoryTheory.AddMon.rightUnitor_neg_hom, CategoryTheory.Functor.mapAddMonCompIso_hom_app_hom, CategoryTheory.AddMon.instIsIsoHom, CategoryTheory.AddMon.associator_neg_hom, CategoryTheory.AddMon.forget_map, ext_iff, CategoryTheory.AddMon.leftUnitor_neg_hom, hom_nsmul, CategoryTheory.AddMon.rightUnitor_hom_hom, CategoryTheory.AddMon.mkIso'_hom_hom, CategoryTheory.AddMon.instIsIsoHomOfMapForget, CategoryTheory.AddMon.fst_hom, CategoryTheory.AddMon.id_hom', CategoryTheory.Functor.mapAddMonIdIso_inv_app_hom, CategoryTheory.yonedaAddMon_map_app, CategoryTheory.AddMon.leftUnitor_hom_hom
mk' 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
ext 📖hom
ext' 📖homext
ext'_iff 📖mathematicalhomext'
ext_iff 📖mathematicalhomext
isAddMonHom_hom 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.AddMon.X
CategoryTheory.AddMon.addMon
hom

CategoryTheory.AddMonObj

Definitions

NameCategoryTheorems
add 📖CompOp
67 mathmath: CategoryTheory.IsAddMonHom.add_hom, CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_hom, CategoryTheory.AddMon.add_def, add_zero_assoc, ofRepresentableBy_add, add_eq_add, add_assoc_assoc, add_add_add_comm'_assoc, zero_add_hom, CategoryTheory.IsCommAddMonObj.add_comm'_assoc, tensorObj.add_def, CategoryTheory.AddMon.tensorObj_add, CategoryTheory.Functor.FullyFaithful.addMonObj_add, add_zero_hom_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.eq_zero_add, CategoryTheory.AddMon.tensorAddUnit_add, CategoryTheory.IsCommAddMonObj.add_comm', add_leftUnitor, add_def, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_neg_tensor_zero_add_assoc, CategoryTheory.AddMon.trivial_addMon_add, lift_lift_assoc, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj_μ, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_neg_zero_tensor_add_assoc, add_assoc, add_braiding, add_associator, CategoryTheory.Functor.obj.σ_def, AddMon_tensor_add_zero, instIsAddMonHomAddOfIsCommAddMonObj, lift_comp_zero_left, zero_add_assoc, CategoryTheory.Functor.comp_mapAddMon_add, add_assoc_flip, zero_add, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_functor_obj_addMon_add, CategoryTheory.Mathlib.Tactic.MonTauto.eq_add_zero, CategoryTheory.Functor.obj.σ_def_assoc, CategoryTheory.Hom.add_def, CategoryTheory.AddMon.hom_add, add_assoc_flip_assoc, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_add, add_add_add_comm', CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_neg_tensor_zero_add, AddMon_tensor_zero_add, lift_comp_zero_right_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_neg_assoc, add_rightUnitor, add_zero_hom, add_zero, add_add_add_comm, lift_comp_zero_left_assoc, CategoryTheory.AddMon.tensor_add, CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_neg, CategoryTheory.Functor.id_mapAddMon_add, zero_add_hom_assoc, lift_comp_zero_right, ofIso_add, add_add_add_comm_assoc, CategoryTheory.IsAddMonHom.add_hom_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_hom_assoc, ext_iff, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_neg_zero_tensor_add, AddMon_tensor_add_assoc, CategoryTheory.Functor.mapAddMon_obj_addMon_add, CategoryTheory.IsCommAddMonObj.add_comm
instTensorAddUnit 📖CompOp
8 mathmath: add_def, zero_def, instIsAddMonHomZero, instIsAddMonHomHomLeftUnitor, CategoryTheory.IsCommAddMonObj.instTensorAddUnit, instIsAddMonHomToAddUnit, instIsAddMonHomHomRightUnitor, CategoryTheory.Functor.instIsAddMonHomε
ofIso 📖CompOp
3 mathmath: ofIso_zero, ofIso_add, CategoryTheory.isAddMonHom_ofIso
termζ 📖CompOp
termσ 📖CompOp
zero 📖CompOp
50 mathmath: tensorObj.zero_def, add_zero_assoc, zero_rightUnitor, zero_leftUnitor, zero_braiding, CategoryTheory.AddMon.trivial_addMon_zero, zero_add_hom, CategoryTheory.Functor.comp_mapAddMon_zero, add_zero_hom_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.eq_zero_add, CategoryTheory.Functor.obj.ζ_def_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_neg_tensor_zero_add_assoc, zero_def, instIsAddMonHomZero, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_neg_zero_tensor_add_assoc, zero_eq_zero, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_functor_obj_addMon_zero, CategoryTheory.Functor.id_mapAddMon_zero, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidal_laxMonoidalToAddMon_obj_zero, AddMon_tensor_add_zero, CategoryTheory.AddMon.tensor_zero, lift_comp_zero_left, ofIso_zero, zero_add_assoc, CategoryTheory.AddMon.hom_zero, zero_add, CategoryTheory.Mathlib.Tactic.MonTauto.eq_add_zero, CategoryTheory.Hom.zero_def, CategoryTheory.IsAddMonHom.zero_hom_assoc, zero_associator, CategoryTheory.AddMon.uniqueHomFromTrivial_default_hom, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_neg_tensor_zero_add, CategoryTheory.AddMon.zero_def, AddMon_tensor_zero_add, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, CategoryTheory.AddMon.tensorObj_zero, lift_comp_zero_right_assoc, add_zero_hom, add_zero, lift_comp_zero_left_assoc, zero_add_hom_assoc, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.addMonToLaxMonoidalObj_ε, lift_comp_zero_right, CategoryTheory.IsAddMonHom.zero_hom, ofRepresentableBy_zero, CategoryTheory.Functor.FullyFaithful.addMonObj_zero, CategoryTheory.Functor.mapAddMon_obj_addMon_zero, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_neg_zero_tensor_add, CategoryTheory.AddMon.tensorAddUnit_zero, CategoryTheory.Functor.obj.ζ_def
«termζ[_]» 📖CompOp
«termσ[_]» 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
AddMon_tensor_add_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategory.comp_whiskerRight_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_comp_assoc
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorμ_natural_left
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
add_assoc
CategoryTheory.MonoidalCategory.tensor_associativity
CategoryTheory.MonoidalCategory.tensorμ_natural_right
CategoryTheory.MonoidalCategory.tensor_whiskerLeft
CategoryTheory.Iso.inv_hom_id_assoc
AddMon_tensor_add_zero 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
zero
CategoryTheory.MonoidalCategory.tensorμ
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.whiskerLeft_comp_assoc
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorμ_natural_right
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
add_zero
CategoryTheory.MonoidalCategory.tensor_right_unitality
AddMon_tensor_zero_add 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
zero
CategoryTheory.MonoidalCategory.tensorμ
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategory.comp_whiskerRight_assoc
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorμ_natural_left
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
zero_add
CategoryTheory.MonoidalCategory.tensor_left_unitality
add_add_add_comm 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
add
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc
CategoryTheory.Category.comp_id
CategoryTheory.Category.assoc
CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_neg
CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_hom
CategoryTheory.MonoidalCategory.id_tensorHom_id
CategoryTheory.Category.id_comp
CategoryTheory.IsCommAddMonObj.add_comm
CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp_assoc
add_add_add_comm' 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorδ
CategoryTheory.MonoidalCategoryStruct.tensorHom
add
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc
CategoryTheory.Category.comp_id
CategoryTheory.Category.assoc
CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_neg
CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_hom
CategoryTheory.MonoidalCategory.id_tensorHom_id
CategoryTheory.Category.id_comp
CategoryTheory.IsCommAddMonObj.add_comm'
CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp_assoc
add_add_add_comm'_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorδ
CategoryTheory.MonoidalCategoryStruct.tensorHom
add
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_add_add_comm'
add_add_add_comm_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
add
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_add_add_comm
add_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
add_assoc_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_assoc
add_assoc_flip 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
add
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
add_assoc
CategoryTheory.Iso.inv_hom_id_assoc
add_assoc_flip_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
add
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_assoc_flip
add_associator 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.MonoidalCategory.associator_naturality
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.associator_monoidal
add_braiding 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
add
CategoryTheory.AddMon.instAddMonObjTensorObj
CategoryTheory.SymmetricCategory.toBraidedCategory
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Category.assoc
CategoryTheory.BraidedCategory.braiding_naturality
CategoryTheory.BraidedCategory.braiding_tensor_right_hom
CategoryTheory.BraidedCategory.braiding_tensor_left_hom
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.MonoidalCategory.whisker_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_comp
CategoryTheory.MonoidalCategory.pentagon_assoc
CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv_assoc
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv_assoc
CategoryTheory.SymmetricCategory.symmetry
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.MonoidalCategory.whiskerLeft_id
CategoryTheory.Category.id_comp
CategoryTheory.MonoidalCategory.pentagon_inv_assoc
CategoryTheory.Iso.hom_inv_id_assoc
CategoryTheory.MonoidalCategory.associator_inv_naturality_left
CategoryTheory.Iso.inv_hom_id
CategoryTheory.MonoidalCategory.associator_naturality_right
CategoryTheory.MonoidalCategory.tensorHom_def
add_def 📖mathematicaladd
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorAddUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategoryStruct.leftUnitor
add_leftUnitor 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
add
CategoryTheory.Category.comp_id
CategoryTheory.Category.id_comp
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.leftUnitor_naturality
CategoryTheory.MonoidalCategory.leftUnitor_monoidal
add_rightUnitor 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.Category.id_comp
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.rightUnitor_naturality
CategoryTheory.MonoidalCategory.rightUnitor_monoidal
add_zero 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
zero
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
add_zero_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
zero
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_zero
add_zero_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
zero
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.tensorHom_def_assoc
add_zero
CategoryTheory.MonoidalCategory.rightUnitor_naturality
add_zero_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
zero
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_zero_hom
ext 📖addCategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.MonoidalCategory.whiskerRight_id
CategoryTheory.MonoidalCategory.unitors_equal
CategoryTheory.Category.assoc
add_zero
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.MonoidalCategory.id_whiskerLeft
zero_add
ext_iff 📖mathematicaladdext
instIsAddMonHomHomAssociator 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorObj.instTensorObj
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
zero_associator
add_associator
instIsAddMonHomHomBraiding 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMon.instAddMonObjTensorObj
CategoryTheory.SymmetricCategory.toBraidedCategory
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
zero_braiding
add_braiding
instIsAddMonHomHomLeftUnitor 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
tensorObj.instTensorObj
instTensorAddUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
zero_leftUnitor
add_leftUnitor
instIsAddMonHomHomRightUnitor 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
tensorObj.instTensorObj
instTensorAddUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
zero_rightUnitor
add_rightUnitor
instIsAddMonHomId 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.Category.id_comp
instIsAddMonHomTensorHom 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorObj.instTensorObj
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.IsAddMonHom.zero_hom
CategoryTheory.MonoidalCategory.tensorμ_natural
CategoryTheory.IsAddMonHom.add_hom
instIsAddMonHomWhiskerLeft 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorObj.instTensorObj
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.IsAddMonHom.zero_hom
instIsAddMonHomTensorHom
instIsAddMonHomId
CategoryTheory.IsAddMonHom.add_hom
instIsAddMonHomWhiskerRight 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorObj.instTensorObj
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.IsAddMonHom.zero_hom
instIsAddMonHomTensorHom
instIsAddMonHomId
CategoryTheory.IsAddMonHom.add_hom
ofIso_add 📖mathematicaladd
ofIso
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.inv
CategoryTheory.Iso.hom
ofIso_zero 📖mathematicalzero
ofIso
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
zero_add 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerRight
zero
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
zero_add_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerRight
zero
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
zero_add
zero_add_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
zero
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategory.tensorHom_def'_assoc
zero_add
CategoryTheory.MonoidalCategory.leftUnitor_naturality
zero_add_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
zero
add
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
zero_add_hom
zero_associator 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
zero
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Category.assoc
CategoryTheory.Iso.cancel_iso_inv_left
CategoryTheory.Category.id_comp
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.MonoidalCategory.associator_naturality
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.id_whiskerLeft
CategoryTheory.Iso.hom_inv_id_assoc
zero_braiding 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
zero
tensorObj.instTensorObj
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.Category.assoc
CategoryTheory.BraidedCategory.braiding_naturality
CategoryTheory.braiding_tensorUnit_right
CategoryTheory.Iso.cancel_iso_inv_left
Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_tensorHom
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.evalHorizontalComp_cons_cons
Mathlib.Tactic.Monoidal.evalHorizontalCompAux_of
Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_cons
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_nil_cons
Mathlib.Tactic.BicategoryLike.mk_eq_of_cons
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_rightUnitor
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_leftUnitor
Mathlib.Tactic.Monoidal.naturality_tensorHom
Mathlib.Tactic.Monoidal.naturality_id
zero_def 📖mathematicalzero
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorAddUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
zero_leftUnitor 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.CategoryStruct.id
zero
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.id_whiskerLeft
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
zero_rightUnitor 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
zero
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.whiskerRight_id
CategoryTheory.MonoidalCategory.unitors_equal
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id

CategoryTheory.AddMonObj.tensorObj

Definitions

NameCategoryTheorems
instTensorObj 📖CompOp
10 mathmath: zero_def, CategoryTheory.AddMonObj.zero_braiding, CategoryTheory.AddMonObj.instIsAddMonHomTensorHom, add_def, CategoryTheory.AddMon.monMonoidalStruct_tensorHom_hom, CategoryTheory.AddMonObj.instIsAddMonHomWhiskerRight, CategoryTheory.AddMonObj.instIsAddMonHomHomLeftUnitor, CategoryTheory.AddMonObj.instIsAddMonHomWhiskerLeft, CategoryTheory.AddMonObj.instIsAddMonHomHomRightUnitor, CategoryTheory.AddMonObj.instIsAddMonHomHomAssociator

Theorems

NameKindAssumesProvesValidatesDepends On
add_def 📖mathematicalCategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
zero_def 📖mathematicalCategoryTheory.AddMonObj.zero
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom

CategoryTheory.Adjunction

Definitions

NameCategoryTheorems
mapAddMon 📖CompOp
2 mathmath: mapAddMon_counit, mapAddMon_unit
mapMon 📖CompOp
2 mathmath: mapMon_unit, mapMon_counit

Theorems

NameKindAssumesProvesValidatesDepends On
mapAddMon_counit 📖mathematicalcounit
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.mapAddMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapAddMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Functor
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.category
CategoryTheory.Functor.comp
CategoryTheory.Functor.LaxMonoidal.comp
CategoryTheory.Functor.id
CategoryTheory.Iso.inv
CategoryTheory.Functor.mapAddMonCompIso
CategoryTheory.Functor.LaxMonoidal.id
CategoryTheory.Functor.mapAddMonNatTrans
IsMonoidal.instIsMonoidalCounit
CategoryTheory.Iso.hom
CategoryTheory.Functor.mapAddMonIdIso
mapAddMon_unit 📖mathematicalunit
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.mapAddMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapAddMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Functor
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.category
CategoryTheory.Functor.id
CategoryTheory.Functor.LaxMonoidal.id
CategoryTheory.Functor.comp
CategoryTheory.Iso.inv
CategoryTheory.Functor.mapAddMonIdIso
CategoryTheory.Functor.LaxMonoidal.comp
CategoryTheory.Functor.mapAddMonNatTrans
IsMonoidal.instIsMonoidalUnit
CategoryTheory.Iso.hom
CategoryTheory.Functor.mapAddMonCompIso
mapMon_counit 📖mathematicalcounit
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.mapMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Functor
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.category
CategoryTheory.Functor.comp
CategoryTheory.Functor.LaxMonoidal.comp
CategoryTheory.Functor.id
CategoryTheory.Iso.inv
CategoryTheory.Functor.mapMonCompIso
CategoryTheory.Functor.LaxMonoidal.id
CategoryTheory.Functor.mapMonNatTrans
IsMonoidal.instIsMonoidalCounit
CategoryTheory.Iso.hom
CategoryTheory.Functor.mapMonIdIso
mapMon_unit 📖mathematicalunit
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.mapMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Functor
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.category
CategoryTheory.Functor.id
CategoryTheory.Functor.LaxMonoidal.id
CategoryTheory.Functor.comp
CategoryTheory.Iso.inv
CategoryTheory.Functor.mapMonIdIso
CategoryTheory.Functor.LaxMonoidal.comp
CategoryTheory.Functor.mapMonNatTrans
IsMonoidal.instIsMonoidalUnit
CategoryTheory.Iso.hom
CategoryTheory.Functor.mapMonCompIso

CategoryTheory.Equivalence

Definitions

NameCategoryTheorems
mapAddMon 📖CompOp
4 mathmath: mapAddMon_inverse, mapAddMon_functor, mapAddMon_counitIso, mapAddMon_unitIso
mapMon 📖CompOp
4 mathmath: mapMon_inverse, mapMon_unitIso, mapMon_counitIso, mapMon_functor

Theorems

NameKindAssumesProvesValidatesDepends On
mapAddMon_counitIso 📖mathematicalcounitIso
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.Iso.trans
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.comp
CategoryTheory.Functor.mapAddMon
inverse
CategoryTheory.Functor.Monoidal.toLaxMonoidal
functor
CategoryTheory.Functor.LaxMonoidal.comp
CategoryTheory.Functor.id
CategoryTheory.Iso.symm
CategoryTheory.Functor.mapAddMonCompIso
CategoryTheory.Functor.LaxMonoidal.id
CategoryTheory.Functor.mapAddMonNatIso
CategoryTheory.Adjunction.Equivalence.instIsMonoidalCounit
CategoryTheory.Functor.mapAddMonIdIso
mapAddMon_functor 📖mathematicalfunctor
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.Functor.mapAddMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapAddMon_inverse 📖mathematicalinverse
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.Functor.mapAddMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapAddMon_unitIso 📖mathematicalunitIso
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.Iso.trans
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.id
CategoryTheory.Functor.mapAddMon
CategoryTheory.Functor.LaxMonoidal.id
CategoryTheory.Functor.comp
functor
CategoryTheory.Functor.Monoidal.toLaxMonoidal
inverse
CategoryTheory.Iso.symm
CategoryTheory.Functor.mapAddMonIdIso
CategoryTheory.Functor.LaxMonoidal.comp
CategoryTheory.Functor.mapAddMonNatIso
CategoryTheory.Adjunction.Equivalence.instIsMonoidalUnit
CategoryTheory.Functor.mapAddMonCompIso
mapMon_counitIso 📖mathematicalcounitIso
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.Iso.trans
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.comp
CategoryTheory.Functor.mapMon
inverse
CategoryTheory.Functor.Monoidal.toLaxMonoidal
functor
CategoryTheory.Functor.LaxMonoidal.comp
CategoryTheory.Functor.id
CategoryTheory.Iso.symm
CategoryTheory.Functor.mapMonCompIso
CategoryTheory.Functor.LaxMonoidal.id
CategoryTheory.Functor.mapMonNatIso
CategoryTheory.Adjunction.Equivalence.instIsMonoidalCounit
CategoryTheory.Functor.mapMonIdIso
mapMon_functor 📖mathematicalfunctor
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.Functor.mapMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapMon_inverse 📖mathematicalinverse
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.Functor.mapMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapMon_unitIso 📖mathematicalunitIso
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.Iso.trans
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.id
CategoryTheory.Functor.mapMon
CategoryTheory.Functor.LaxMonoidal.id
CategoryTheory.Functor.comp
functor
CategoryTheory.Functor.Monoidal.toLaxMonoidal
inverse
CategoryTheory.Iso.symm
CategoryTheory.Functor.mapMonIdIso
CategoryTheory.Functor.LaxMonoidal.comp
CategoryTheory.Functor.mapMonNatIso
CategoryTheory.Adjunction.Equivalence.instIsMonoidalUnit
CategoryTheory.Functor.mapMonCompIso

CategoryTheory.Functor

Definitions

NameCategoryTheorems
addMonObjObj 📖CompOp
13 mathmath: instIsAddMonHomμ, map_add', obj.ζ_def_assoc, obj.σ_def, mapAddMon_map_hom, FullyFaithful.homAddEquiv_symm_apply, obj.σ_def_assoc, map.instIsAddMonHom, map_zero', homAddMonoidHom_apply, instIsAddMonHomε, FullyFaithful.homAddEquiv_apply, obj.ζ_def
instBraidedMonMapAddMon 📖CompOp
instBraidedMonMapMon 📖CompOp
instLaxBraidedMonMapAddMon 📖CompOp
instLaxBraidedMonMapMon 📖CompOp
instLaxMonoidalMonMapAddMon 📖CompOp
instLaxMonoidalMonMapMon 📖CompOp
instMonoidalMonMapAddMon 📖CompOp
instMonoidalMonMapMon 📖CompOp
mapAddMon 📖CompOp
28 mathmath: CategoryTheory.Equivalence.mapAddMon_inverse, CategoryTheory.Equivalence.mapAddMon_functor, mapAddMon_obj_X, comp_mapAddMon_zero, mapAddMonFunctor_map_app_hom, essImage_mapAddMon, mapAddMonCompIso_inv_app_hom, id_mapAddMon_zero, mapAddMon_map_hom, mapAddMonIdIso_hom_app_hom, CategoryTheory.Adjunction.mapAddMon_counit, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_obj, comp_mapAddMon_add, Full.mapAddMon, CategoryTheory.Equivalence.mapAddMon_counitIso, mapAddMonNatIso_hom_app_hom, mapAddMonNatTrans_app_hom, mapAddMonFunctor_obj, mapAddMonNatIso_inv_app_hom, FullyFaithful.mapAddMon_preimage_hom, mapAddMonCompIso_hom_app_hom, id_mapAddMon_add, CategoryTheory.Adjunction.mapAddMon_unit, CategoryTheory.Equivalence.mapAddMon_unitIso, Faithful.mapAddMon, mapAddMon_obj_addMon_zero, mapAddMonIdIso_inv_app_hom, mapAddMon_obj_addMon_add
mapAddMonCompIso 📖CompOp
6 mathmath: mapAddMonCompIso_inv_app_hom, CategoryTheory.Adjunction.mapAddMon_counit, CategoryTheory.Equivalence.mapAddMon_counitIso, mapAddMonCompIso_hom_app_hom, CategoryTheory.Adjunction.mapAddMon_unit, CategoryTheory.Equivalence.mapAddMon_unitIso
mapAddMonFunctor 📖CompOp
4 mathmath: mapAddMonFunctor_map_app_hom, mapAddMonFunctor_obj, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_functor_map_hom, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_map
mapAddMonIdIso 📖CompOp
6 mathmath: mapAddMonIdIso_hom_app_hom, CategoryTheory.Adjunction.mapAddMon_counit, CategoryTheory.Equivalence.mapAddMon_counitIso, CategoryTheory.Adjunction.mapAddMon_unit, CategoryTheory.Equivalence.mapAddMon_unitIso, mapAddMonIdIso_inv_app_hom
mapAddMonNatIso 📖CompOp
4 mathmath: CategoryTheory.Equivalence.mapAddMon_counitIso, mapAddMonNatIso_hom_app_hom, mapAddMonNatIso_inv_app_hom, CategoryTheory.Equivalence.mapAddMon_unitIso
mapAddMonNatTrans 📖CompOp
3 mathmath: CategoryTheory.Adjunction.mapAddMon_counit, mapAddMonNatTrans_app_hom, CategoryTheory.Adjunction.mapAddMon_unit
mapMon 📖CompOp
39 mathmath: mapMonNatTrans_app_hom, FullyFaithful.mapMon_preimage_hom, CategoryTheory.Equivalence.mapMon_inverse, mapCommMon_obj_mon_mul, CategoryTheory.Adjunction.mapMon_unit, FullyFaithful.mapGrp_preimage, mapMon_obj_mon_mul, mapMonCompIso_hom_app_hom, CategoryTheory.Equivalence.mapMon_unitIso, mapMon_obj_X, mapMonNatIso_hom_app_hom, mapMonNatIso_inv_app_hom, CategoryTheory.Adjunction.mapMon_counit, mapMonFunctor_obj, comp_mapMon_mul, mapMonFunctor_map_app_hom, mapMon_obj_mon_one, mapMonIdIso_hom_app_hom, mapCommMon_map_hom_hom, FullyFaithful.mapCommMon_preimage, mapGrp_map_hom_hom, mapMonIdIso_inv_app_hom, CategoryTheory.Equivalence.mapMon_counitIso, mapCommMon_obj_mon_one, CategoryTheory.Bimon.ofMonComon_map_hom, Full.mapMon, mapMon_map_hom, FullyFaithful.mapCommGrp_preimage, id_mapMon_mul, CategoryTheory.Equivalence.mapMon_functor, mapMonCompIso_inv_app_hom, mapGrpNatTrans_app_hom_hom, essImage_mapMon, mapCommGrp_map_hom_hom_hom, mapCommGrpNatTrans_app_hom_hom_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_obj, id_mapMon_one, comp_mapMon_one, Faithful.mapMon
mapMonCompIso 📖CompOp
6 mathmath: CategoryTheory.Adjunction.mapMon_unit, mapMonCompIso_hom_app_hom, CategoryTheory.Equivalence.mapMon_unitIso, CategoryTheory.Adjunction.mapMon_counit, CategoryTheory.Equivalence.mapMon_counitIso, mapMonCompIso_inv_app_hom
mapMonFunctor 📖CompOp
4 mathmath: mapMonFunctor_obj, mapMonFunctor_map_app_hom, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_functor_map_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_map
mapMonIdIso 📖CompOp
6 mathmath: CategoryTheory.Adjunction.mapMon_unit, CategoryTheory.Equivalence.mapMon_unitIso, CategoryTheory.Adjunction.mapMon_counit, mapMonIdIso_hom_app_hom, mapMonIdIso_inv_app_hom, CategoryTheory.Equivalence.mapMon_counitIso
mapMonNatIso 📖CompOp
4 mathmath: CategoryTheory.Equivalence.mapMon_unitIso, mapMonNatIso_hom_app_hom, mapMonNatIso_inv_app_hom, CategoryTheory.Equivalence.mapMon_counitIso
mapMonNatTrans 📖CompOp
3 mathmath: mapMonNatTrans_app_hom, CategoryTheory.Adjunction.mapMon_unit, CategoryTheory.Adjunction.mapMon_counit
monObjObj 📖CompOp
14 mathmath: map_mul, FullyFaithful.homMulEquiv_apply, instIsMonHomμ, map.instIsMonHom, obj.η_def_assoc, obj.η_def, isCommMonObj_obj, FullyFaithful.homMulEquiv_symm_apply, obj.μ_def, instIsMonHomε, mapMon_map_hom, obj.μ_def_assoc, homMonoidHom_apply, map_one

Theorems

NameKindAssumesProvesValidatesDepends On
comp_mapAddMon_add 📖mathematicalCategoryTheory.AddMonObj.add
CategoryTheory.AddMon.X
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
comp
LaxMonoidal.comp
CategoryTheory.AddMon.addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
LaxMonoidal.μ
map
comp_mapAddMon_zero 📖mathematicalCategoryTheory.AddMonObj.zero
CategoryTheory.AddMon.X
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
comp
LaxMonoidal.comp
CategoryTheory.AddMon.addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
LaxMonoidal.ε
map
comp_mapMon_mul 📖mathematicalCategoryTheory.MonObj.mul
CategoryTheory.Mon.X
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
comp
LaxMonoidal.comp
CategoryTheory.Mon.mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
LaxMonoidal.μ
map
comp_mapMon_one 📖mathematicalCategoryTheory.MonObj.one
CategoryTheory.Mon.X
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
comp
LaxMonoidal.comp
CategoryTheory.Mon.mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
LaxMonoidal.ε
map
essImage_mapAddMon 📖mathematicalessImage
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
Monoidal.toLaxMonoidal
CategoryTheory.AddMon.X
FullyFaithful.map_preimage
Monoidal.ε_η_assoc
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
Monoidal.μ_δ_assoc
essImage_mapMon 📖mathematicalessImage
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
Monoidal.toLaxMonoidal
CategoryTheory.Mon.X
FullyFaithful.map_preimage
Monoidal.ε_η_assoc
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
Monoidal.μ_δ_assoc
id_mapAddMon_add 📖mathematicalCategoryTheory.AddMonObj.add
CategoryTheory.AddMon.X
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
id
LaxMonoidal.id
CategoryTheory.AddMon.addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.id
id_mapAddMon_zero 📖mathematicalCategoryTheory.AddMonObj.zero
CategoryTheory.AddMon.X
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
id
LaxMonoidal.id
CategoryTheory.AddMon.addMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.id
id_mapMon_mul 📖mathematicalCategoryTheory.MonObj.mul
CategoryTheory.Mon.X
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
id
LaxMonoidal.id
CategoryTheory.Mon.mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.id
id_mapMon_one 📖mathematicalCategoryTheory.MonObj.one
CategoryTheory.Mon.X
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
id
LaxMonoidal.id
CategoryTheory.Mon.mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.id
instIsAddMonHomε 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
obj
CategoryTheory.AddMonObj.instTensorAddUnit
addMonObjObj
LaxMonoidal.ε
CategoryTheory.Category.id_comp
map_id
CategoryTheory.Category.comp_id
LaxMonoidal.ε_tensorHom_comp_μ_assoc
CategoryTheory.MonoidalCategory.id_whiskerLeft
LaxMonoidal.left_unitality
CategoryTheory.Iso.map_inv_hom_id
CategoryTheory.Category.assoc
LaxMonoidal.left_unitality_inv_assoc
instIsAddMonHomμ 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
obj
CategoryTheory.AddMon.instAddMonObjTensorObj
addMonObjObj
LaxBraided.toLaxMonoidal
LaxMonoidal.μ
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom_assoc
CategoryTheory.Category.assoc
LaxMonoidal.μ_natural
LaxMonoidal.left_unitality_inv_assoc
map_comp
CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc
instIsMonHomε 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
obj
CategoryTheory.MonObj.instTensorUnit
monObjObj
LaxMonoidal.ε
CategoryTheory.Category.id_comp
map_id
CategoryTheory.Category.comp_id
LaxMonoidal.ε_tensorHom_comp_μ_assoc
CategoryTheory.MonoidalCategory.id_whiskerLeft
LaxMonoidal.left_unitality
CategoryTheory.Iso.map_inv_hom_id
CategoryTheory.Category.assoc
LaxMonoidal.left_unitality_inv_assoc
instIsMonHomμ 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
obj
CategoryTheory.Mon.instMonObjTensorObj
monObjObj
LaxBraided.toLaxMonoidal
LaxMonoidal.μ
CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom_assoc
CategoryTheory.Category.assoc
LaxMonoidal.μ_natural
LaxMonoidal.left_unitality_inv_assoc
CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc
map_comp
mapAddMonCompIso_hom_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
comp
LaxMonoidal.comp
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
mapAddMonCompIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.X
mapAddMonCompIso_inv_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
comp
mapAddMon
LaxMonoidal.comp
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
mapAddMonCompIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.X
mapAddMonFunctor_map_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.NatTrans.app
map
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor
category
mapAddMonFunctor
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.AddMon.X
mapAddMonFunctor_obj 📖mathematicalobj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
category
mapAddMonFunctor
mapAddMon
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
mapAddMonIdIso_hom_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
id
LaxMonoidal.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
mapAddMonIdIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.X
mapAddMonIdIso_inv_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
id
mapAddMon
LaxMonoidal.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
mapAddMonIdIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.X
mapAddMonNatIso_hom_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
mapAddMonNatIso
CategoryTheory.AddMon.X
mapAddMonNatIso_inv_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
mapAddMonNatIso
CategoryTheory.AddMon.X
mapAddMonNatTrans_app_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.NatTrans.app
mapAddMonNatTrans
CategoryTheory.AddMon.X
mapAddMon_map_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
obj
CategoryTheory.AddMon.X
addMonObjObj
CategoryTheory.AddMon.addMon
map
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
mapAddMon_obj_X 📖mathematicalCategoryTheory.AddMon.X
obj
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
mapAddMon_obj_addMon_add 📖mathematicalCategoryTheory.AddMonObj.add
obj
CategoryTheory.AddMon.X
CategoryTheory.AddMon.addMon
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
LaxMonoidal.μ
map
mapAddMon_obj_addMon_zero 📖mathematicalCategoryTheory.AddMonObj.zero
obj
CategoryTheory.AddMon.X
CategoryTheory.AddMon.addMon
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
mapAddMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
LaxMonoidal.ε
map
mapMonCompIso_hom_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
comp
LaxMonoidal.comp
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
mapMonCompIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.X
mapMonCompIso_inv_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
comp
mapMon
LaxMonoidal.comp
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
mapMonCompIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.X
mapMonFunctor_map_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.NatTrans.app
map
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor
category
mapMonFunctor
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Mon.X
mapMonFunctor_obj 📖mathematicalobj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
category
mapMonFunctor
mapMon
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
mapMonIdIso_hom_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
id
LaxMonoidal.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
mapMonIdIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.X
mapMonIdIso_inv_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
id
mapMon
LaxMonoidal.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
mapMonIdIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.X
mapMonNatIso_hom_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
mapMonNatIso
CategoryTheory.Mon.X
mapMonNatIso_inv_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
mapMonNatIso
CategoryTheory.Mon.X
mapMonNatTrans_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.NatTrans.app
mapMonNatTrans
CategoryTheory.Mon.X
mapMon_map_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
obj
CategoryTheory.Mon.X
monObjObj
CategoryTheory.Mon.mon
map
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
mapMon_obj_X 📖mathematicalCategoryTheory.Mon.X
obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
mapMon_obj_mon_mul 📖mathematicalCategoryTheory.MonObj.mul
obj
CategoryTheory.Mon.X
CategoryTheory.Mon.mon
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
LaxMonoidal.μ
map
mapMon_obj_mon_one 📖mathematicalCategoryTheory.MonObj.one
obj
CategoryTheory.Mon.X
CategoryTheory.Mon.mon
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
mapMon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
LaxMonoidal.ε
map

CategoryTheory.Functor.Faithful

Theorems

NameKindAssumesProvesValidatesDepends On
mapAddMon 📖mathematicalCategoryTheory.Functor.Faithful
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.mapAddMon
CategoryTheory.AddMon.Hom.ext
map_injective
mapMon 📖mathematicalCategoryTheory.Functor.Faithful
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.mapMon
CategoryTheory.Mon.Hom.ext
map_injective

CategoryTheory.Functor.Full

Theorems

NameKindAssumesProvesValidatesDepends On
mapAddMon 📖mathematicalCategoryTheory.Functor.Full
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.mapAddMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
CategoryTheory.Functor.map_surjective
CategoryTheory.Functor.map_injective
CategoryTheory.Functor.map_comp
CategoryTheory.Category.assoc
CategoryTheory.cancel_epi
CategoryTheory.epi_of_strongEpi
CategoryTheory.strongEpi_of_isIso
CategoryTheory.Functor.Monoidal.instIsIsoε
CategoryTheory.IsAddMonHom.zero_hom
CategoryTheory.AddMon.instIsAddMonHomHom
CategoryTheory.Functor.LaxMonoidal.μ_natural_assoc
CategoryTheory.Functor.Monoidal.instIsIsoμ
CategoryTheory.IsAddMonHom.add_hom
CategoryTheory.AddMon.Hom.ext
mapMon 📖mathematicalCategoryTheory.Functor.Full
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.mapMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
CategoryTheory.Functor.map_surjective
CategoryTheory.Functor.map_injective
CategoryTheory.Functor.map_comp
CategoryTheory.Category.assoc
CategoryTheory.epi_of_strongEpi
CategoryTheory.strongEpi_of_isIso
CategoryTheory.Functor.Monoidal.instIsIsoε
CategoryTheory.IsMonHom.one_hom
CategoryTheory.Mon.instIsMonHomHom
CategoryTheory.Functor.LaxMonoidal.μ_natural_assoc
CategoryTheory.Functor.Monoidal.instIsIsoμ
CategoryTheory.IsMonHom.mul_hom
CategoryTheory.Mon.Hom.ext

CategoryTheory.Functor.FullyFaithful

Definitions

NameCategoryTheorems
addMonObj 📖CompOp
2 mathmath: addMonObj_add, addMonObj_zero
mapAddMon 📖CompOp
1 mathmath: mapAddMon_preimage_hom
mapMon 📖CompOp
4 mathmath: mapMon_preimage_hom, mapGrp_preimage, mapCommMon_preimage, mapCommGrp_preimage
monObj 📖CompOp
2 mathmath: monObj_mul, monObj_one

Theorems

NameKindAssumesProvesValidatesDepends On
addMonObj_add 📖mathematicalCategoryTheory.AddMonObj.add
addMonObj
preimage
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Functor.OplaxMonoidal.δ
addMonObj_zero 📖mathematicalCategoryTheory.AddMonObj.zero
addMonObj
preimage
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Functor.OplaxMonoidal.η
isAddMonHom_preimage 📖mathematicalCategoryTheory.IsAddMonHom
preimage
map_injective
CategoryTheory.Functor.map_comp
map_preimage
CategoryTheory.cancel_epi
CategoryTheory.epi_of_strongEpi
CategoryTheory.strongEpi_of_isIso
CategoryTheory.Functor.Monoidal.instIsIsoε
CategoryTheory.IsAddMonHom.zero_hom
CategoryTheory.Functor.Monoidal.instIsIsoμ
CategoryTheory.IsAddMonHom.add_hom
isMonHom_preimage 📖mathematicalCategoryTheory.IsMonHom
preimage
map_injective
CategoryTheory.Functor.map_comp
map_preimage
CategoryTheory.cancel_epi
CategoryTheory.epi_of_strongEpi
CategoryTheory.strongEpi_of_isIso
CategoryTheory.Functor.Monoidal.instIsIsoε
CategoryTheory.IsMonHom.one_hom
CategoryTheory.Functor.Monoidal.instIsIsoμ
CategoryTheory.IsMonHom.mul_hom
mapAddMon_preimage_hom 📖mathematicalCategoryTheory.AddMon.Hom.hom
preimage
CategoryTheory.AddMon
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor.mapAddMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapAddMon
CategoryTheory.AddMon.X
CategoryTheory.Functor.obj
mapMon_preimage_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
preimage
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.mapMon
CategoryTheory.Functor.Monoidal.toLaxMonoidal
mapMon
CategoryTheory.Mon.X
CategoryTheory.Functor.obj
monObj_mul 📖mathematicalCategoryTheory.MonObj.mul
monObj
preimage
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Functor.OplaxMonoidal.δ
monObj_one 📖mathematicalCategoryTheory.MonObj.one
monObj
preimage
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Functor.OplaxMonoidal.η

CategoryTheory.Functor.map

Theorems

NameKindAssumesProvesValidatesDepends On
instIsAddMonHom 📖mathematicalCategoryTheory.IsAddMonHom
CategoryTheory.Functor.obj
CategoryTheory.Functor.addMonObjObj
CategoryTheory.Functor.map
CategoryTheory.Category.assoc
CategoryTheory.Functor.map_comp
CategoryTheory.IsAddMonHom.zero_hom
CategoryTheory.IsAddMonHom.add_hom
CategoryTheory.Functor.LaxMonoidal.μ_natural_assoc
instIsMonHom 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.Functor.obj
CategoryTheory.Functor.monObjObj
CategoryTheory.Functor.map
CategoryTheory.Category.assoc
CategoryTheory.IsMonHom.one_hom
CategoryTheory.IsMonHom.mul_hom
CategoryTheory.Functor.LaxMonoidal.μ_natural_assoc

CategoryTheory.Functor.obj

Theorems

NameKindAssumesProvesValidatesDepends On
ζ_def 📖mathematicalCategoryTheory.AddMonObj.zero
CategoryTheory.Functor.obj
CategoryTheory.Functor.addMonObjObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.map
ζ_def_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.AddMonObj.zero
CategoryTheory.Functor.addMonObjObj
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.map
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
ζ_def
η_def 📖mathematicalCategoryTheory.MonObj.one
CategoryTheory.Functor.obj
CategoryTheory.Functor.monObjObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.map
η_def_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.MonObj.one
CategoryTheory.Functor.monObjObj
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.map
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
η_def
μ_def 📖mathematicalCategoryTheory.MonObj.mul
CategoryTheory.Functor.obj
CategoryTheory.Functor.monObjObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Functor.map
μ_def_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.MonObj.mul
CategoryTheory.Functor.monObjObj
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Functor.map
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
μ_def
σ_def 📖mathematicalCategoryTheory.AddMonObj.add
CategoryTheory.Functor.obj
CategoryTheory.Functor.addMonObjObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Functor.map
σ_def_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.AddMonObj.add
CategoryTheory.Functor.addMonObjObj
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Functor.map
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
σ_def

CategoryTheory.IsAddMonHom

Theorems

NameKindAssumesProvesValidatesDepends On
add_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategoryStruct.tensorHom
add_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_hom
zero_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMonObj.zero
zero_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMonObj.zero
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
zero_hom

CategoryTheory.IsCommAddMonObj

Theorems

NameKindAssumesProvesValidatesDepends On
add_comm 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.AddMonObj.add
add_comm' 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.BraidedCategory.braiding
CategoryTheory.AddMonObj.add
CategoryTheory.cancel_epi
CategoryTheory.epi_of_strongEpi
CategoryTheory.strongEpi_of_isIso
CategoryTheory.Iso.isIso_hom
CategoryTheory.Iso.hom_inv_id_assoc
add_comm
add_comm'_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.BraidedCategory.braiding
CategoryTheory.AddMonObj.add
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_comm'
instTensorAddUnit 📖mathematicalCategoryTheory.IsCommAddMonObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMonObj.instTensorAddUnit
CategoryTheory.braiding_leftUnitor
CategoryTheory.MonoidalCategory.unitors_equal

CategoryTheory.IsCommMonObj

Theorems

NameKindAssumesProvesValidatesDepends On
instTensorUnit 📖mathematicalCategoryTheory.IsCommMonObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonObj.instTensorUnit
CategoryTheory.braiding_leftUnitor
CategoryTheory.MonoidalCategory.unitors_equal
mul_comm 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonObj.mul
mul_comm' 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonObj.mul
CategoryTheory.cancel_epi
CategoryTheory.epi_of_strongEpi
CategoryTheory.strongEpi_of_isIso
CategoryTheory.Iso.isIso_hom
CategoryTheory.Iso.hom_inv_id_assoc
mul_comm
mul_comm'_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonObj.mul
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_comm'
mul_comm_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonObj.mul
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_comm

CategoryTheory.IsMonHom

Theorems

NameKindAssumesProvesValidatesDepends On
mul_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategoryStruct.tensorHom
mul_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_hom
one_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonObj.one
one_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonObj.one
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
one_hom

CategoryTheory.Mathlib.Tactic.MonTauto

Theorems

NameKindAssumesProvesValidatesDepends On
add_assoc_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMonObj.add
CategoryTheory.CategoryStruct.id
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.MonoidalCategory.whiskerRight_tensor
CategoryTheory.Category.assoc
CategoryTheory.Iso.hom_inv_id_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_id
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.AddMonObj.add_assoc
add_assoc_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMonObj.add
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_assoc_hom
add_assoc_neg 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMonObj.add
CategoryTheory.CategoryStruct.id
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.MonoidalCategory.tensor_whiskerLeft
CategoryTheory.Category.assoc
CategoryTheory.AddMonObj.add_assoc
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.whiskerLeft_comp
add_assoc_neg_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMonObj.add
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_assoc_neg
associator_hom_comp_tensorHom_tensorHom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonoidalCategory.associator_conjugation
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
associator_hom_comp_tensorHom_tensorHom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
associator_hom_comp_tensorHom_tensorHom
associator_hom_comp_tensorHom_tensorHom_comp 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.CategoryStruct.id
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.whiskerRight_tensor
CategoryTheory.MonoidalCategory.whiskerLeft_comp
CategoryTheory.Iso.hom_inv_id_assoc
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.MonoidalCategory.whisker_assoc
CategoryTheory.MonoidalCategory.tensor_whiskerLeft
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.Category.id_comp
CategoryTheory.Iso.inv_hom_id
associator_hom_comp_tensorHom_tensorHom_comp_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
associator_hom_comp_tensorHom_tensorHom_comp
associator_inv_comp_tensorHom_tensorHom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonoidalCategory.associator_conjugation
CategoryTheory.Iso.inv_hom_id_assoc
associator_inv_comp_tensorHom_tensorHom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
associator_inv_comp_tensorHom_tensorHom
associator_inv_comp_tensorHom_tensorHom_comp 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.CategoryStruct.id
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensor_whiskerLeft
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.MonoidalCategory.whisker_assoc
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_comp
CategoryTheory.MonoidalCategory.whiskerRight_tensor
CategoryTheory.MonoidalCategory.whiskerLeft_id
CategoryTheory.Category.id_comp
CategoryTheory.Iso.hom_inv_id_assoc
associator_inv_comp_tensorHom_tensorHom_comp_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
associator_inv_comp_tensorHom_tensorHom_comp
eq_add_zero 📖mathematicalCategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.CategoryStruct.id
CategoryTheory.AddMonObj.zero
CategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.AddMonObj.add_zero
eq_mul_one 📖mathematicalCategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.CategoryStruct.id
CategoryTheory.MonObj.one
CategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonObj.mul_one
eq_one_mul 📖mathematicalCategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.one
CategoryTheory.CategoryStruct.id
CategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonObj.one_mul
eq_zero_add 📖mathematicalCategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMonObj.zero
CategoryTheory.CategoryStruct.id
CategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.AddMonObj.zero_add
leftUnitor_inv_one_tensor_mul 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.one
CategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.MonoidalCategory.id_whiskerLeft
CategoryTheory.Category.assoc
CategoryTheory.MonObj.one_mul
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.inv_hom_id_assoc
leftUnitor_inv_one_tensor_mul_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.one
CategoryTheory.MonObj.mul
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
leftUnitor_inv_one_tensor_mul
leftUnitor_neg_zero_tensor_add 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMonObj.zero
CategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.MonoidalCategory.id_whiskerLeft
CategoryTheory.Category.assoc
CategoryTheory.AddMonObj.zero_add
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.inv_hom_id_assoc
leftUnitor_neg_zero_tensor_add_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMonObj.zero
CategoryTheory.AddMonObj.add
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
leftUnitor_neg_zero_tensor_add
mul_assoc_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.mul
CategoryTheory.CategoryStruct.id
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.MonoidalCategory.whiskerRight_tensor
CategoryTheory.Category.assoc
CategoryTheory.Iso.hom_inv_id_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_id
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.MonObj.mul_assoc
mul_assoc_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.mul
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_assoc_hom
mul_assoc_inv 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.mul
CategoryTheory.CategoryStruct.id
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.MonoidalCategory.tensor_whiskerLeft
CategoryTheory.Category.assoc
CategoryTheory.MonObj.mul_assoc
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.whiskerLeft_comp
mul_assoc_inv_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.mul
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_assoc_inv
rightUnitor_inv_tensor_one_mul 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.one
CategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.MonoidalCategory.whiskerRight_id
CategoryTheory.Category.assoc
CategoryTheory.MonObj.mul_one
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.inv_hom_id_assoc
rightUnitor_inv_tensor_one_mul_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.one
CategoryTheory.MonObj.mul
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
rightUnitor_inv_tensor_one_mul
rightUnitor_neg_tensor_zero_add 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMonObj.zero
CategoryTheory.AddMonObj.add
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.MonoidalCategory.whiskerRight_id
CategoryTheory.Category.assoc
CategoryTheory.AddMonObj.add_zero
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.inv_hom_id_assoc
rightUnitor_neg_tensor_zero_add_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.AddMonObj.zero
CategoryTheory.AddMonObj.add
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
rightUnitor_neg_tensor_zero_add

CategoryTheory.Mon

Definitions

NameCategoryTheorems
X 📖CompOp
242 mathmath: CategoryTheory.Grp.Hom.hom_div, id_hom, CategoryTheory.Grp.instIsIsoHomHomMon, CategoryTheory.Bimon.toMonComonObj_mon_mul_hom, CategoryTheory.Functor.mapMonNatTrans_app_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, Bimod.TensorBimod.π_tensor_id_actRight, Bimod.AssociatorBimod.hom_left_act_hom', CategoryTheory.Functor.FullyFaithful.mapMon_preimage_hom, CategoryTheory.CommMon.comp_hom, Bimod.RightUnitorBimod.hom_right_act_hom', Bimod.LeftUnitorBimod.hom_right_act_hom', CategoryTheory.Grp.Hom.hom_hom_zpow, CategoryTheory.Monad.ofMon_η, EquivLaxMonoidalFunctorPUnit.isMonHom_counitIsoAux, forget_obj, leftUnitor_inv_hom, CategoryTheory.Functor.mapCommMon_obj_mon_mul, forget_μ, CategoryTheory.Bimon.ofMonComonObjX_mul, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, hom_injective, Bimod.whiskerLeft_hom, CategoryTheory.Functor.mapMon_obj_mon_mul, CategoryTheory.Grp.trivial_grp_inv, CategoryTheory.shrinkYonedaMonObjObjEquiv_symm_comp, Bimod.TensorBimod.right_assoc', instIsMonHomHom, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, CategoryTheory.Grp.whiskerLeft_hom_hom, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_hom, Bimod.TensorBimod.whiskerLeft_π_actLeft, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, Bimod.actRight_one, CategoryTheory.Bimon.instIsMonHomComonHomEquivMonComonCounitIsoAppX, CategoryTheory.Bimon.instIsComonHomHomEquivMonComonCounitIsoAppXAux, CategoryTheory.Bimon.equivMonComonUnitIsoApp_hom_hom_hom, rightUnitor_inv_hom, Bimod.left_assoc_assoc, CategoryTheory.Bimon.mk'X_X, Bimod.right_assoc, mkIso_hom_hom, CategoryTheory.Bimon.trivial_X_X, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, CategoryTheory.Bimon.ofMonComonObj_comon_comul_hom, equivLaxMonoidalFunctorPUnit_functor_obj_X, Bimod.TensorBimod.actRight_one', CategoryTheory.Functor.mapMonCompIso_hom_app_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, CategoryTheory.Grp.Hom.hom_zpow, CategoryTheory.Bimon.toComon_obj_X, equivLaxMonoidalFunctorPUnit_functor_obj_mon_mul, CategoryTheory.Comon.MonOpOpToComon_map_hom, MonObj.mopEquiv_functor_obj_mon_one_unmop, CategoryTheory.Grp.Hom.hom_hom_div, tensorObj_one, lift_hom, whiskerRight_hom, CategoryTheory.CommMon.instIsIsoHomHomMon, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_inv, Bimod.TensorBimod.middle_assoc', tensorUnit_X, limit_mon_mul, CategoryTheory.Functor.mapMon_obj_X, CategoryTheory.Grp.whiskerRight_hom_hom, commBialgCatEquivComonCommAlgCat_functor_obj_unop_X, CategoryTheory.Functor.mapMonNatIso_hom_app_hom, CategoryTheory.Grp.Hom.hom_hom_inv, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, Bimod.right_assoc_assoc, fst_hom, CategoryTheory.Functor.mapMonNatIso_inv_app_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_obj, Bimod.Hom.left_act_hom, mkIso_inv_hom, CategoryTheory.Grp.whiskerLeft_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.Functor.comp_mapMon_mul, CategoryTheory.yonedaMon_map_app, associator_hom_hom, ModuleCat.MonModuleEquivalenceAlgebra.functor_map_hom_apply, MonObj.mopEquiv_inverse_map_hom, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, comp_hom'_assoc, Bimod.middle_assoc_assoc, CategoryTheory.Comon.MonOpOpToComonObj_comon_comul, ModuleCat.MonModuleEquivalenceAlgebra.functor_obj_carrier, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_obj, CategoryTheory.Functor.mapMonFunctor_map_app_hom, CategoryTheory.CommMon.toMon_X, CategoryTheory.Functor.mapMon_obj_mon_one, CategoryTheory.shrinkYonedaMon_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Functor.mapMonIdIso_hom_app_hom, Bimod.one_actLeft_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_map_app_hom, CategoryTheory.Grp.forget₂Mon_obj_mul, MonObj.mopEquiv_inverse_obj_X, tensorObj_mul, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_map_hom_app, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_counit, whiskerLeft_hom, CategoryTheory.Grp.toMon_X, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_inv, EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, Hom.hom_mul, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_X, CategoryTheory.Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_map, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_μ, associator_inv_hom, CategoryTheory.CommMon.forget₂Mon_obj_mul, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_hom_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, equivLaxMonoidalFunctorPUnit_inverse_obj_map, Bimod.regular_X, uniqueHomFromTrivial_default_hom, EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, MonObj.mopEquiv_functor_map_hom_unmop, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.Bimon.equivMonComonUnitIsoApp_inv_hom_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, CategoryTheory.Grp.comp_hom_hom, CategoryTheory.Functor.mapMonIdIso_inv_app_hom, Bimod.one_actLeft, instIsCommMonObjOppositeCommAlgCatXUnopMonObjCommBialgCatFunctorCommBialgCatEquivComonCommAlgCatOfIsCocommCarrier, CategoryTheory.Bimon.ofMonComonObj_comon_counit_hom, Bimod.TensorBimod.left_assoc', MonObj.mopEquiv_unitIso_hom_app_hom, CategoryTheory.Functor.mapCommMon_obj_mon_one, tensorUnit_one, MonObj.mopEquiv_functor_obj_X_unmop, Hom.hom_pow, CategoryTheory.Grp.forget₂Mon_obj_X, Bimod.left_assoc, Bimod.regular_actRight, Bimod.Hom.left_act_hom_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_X, CategoryTheory.Comon.monoidal_tensorUnit_comon_comul, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, CategoryTheory.Bimon.ofMonComonObjX_one, CategoryTheory.Functor.mapMon_map_hom, leftUnitor_hom_hom, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_inv_hom, EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, CategoryTheory.Bimon.toMonComonObj_mon_one_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_mul, CategoryTheory.Functor.id_mapMon_mul, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, Bimod.RightUnitorBimod.hom_left_act_hom', MonObj.mopEquiv_functor_obj_mon_mul_unmop, equivLaxMonoidalFunctorPUnit_inverse_obj_obj, CategoryTheory.Monad.ofMon_μ, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isAddCommGroup, CategoryTheory.Functor.mapMonCompIso_inv_app_hom, limit_X, CategoryTheory.Grp.trivial_grp_one, CategoryTheory.Bimon.equivMonComonCounitIsoApp_hom_hom_hom, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_comul, CategoryTheory.Grp.forget₂Mon_obj_one, CategoryTheory.Mod_.trivialAction_X, Bimod.actRight_one_assoc, CategoryTheory.Bimon.ofMonComonObjX_X, Bimod.middle_assoc, CategoryTheory.Comon.MonOpOpToComonObj_X, comp_hom', CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, braiding_inv_hom, CategoryTheory.Functor.essImage_mapMon, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, commBialgCatEquivComonCommAlgCat_inverse_obj, hom_mul, CategoryTheory.Monad.ofMon_obj, Bimod.TensorBimod.one_act_left', comp_hom, trivial_X, CategoryTheory.Grp.Hom.hom_inv, limit_mon_one, MonObj.mopEquiv_inverse_obj_mon_one, Bimod.whiskerRight_hom, forget_δ, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, rightUnitor_hom_hom, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_carrier, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, CategoryTheory.shrinkYonedaMon_obj_map_shrinkYonedaMonObjObjEquiv_symm, Bimod.Hom.right_act_hom, instIsIsoHom, equivLaxMonoidalFunctorPUnit_functor_obj_mon_one, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, CategoryTheory.Monad.toMon_X, Hom.isMonHom_hom, Bimod.regular_actLeft, CategoryTheory.Comon.monoidal_tensorUnit_comon_counit, MonObj.mopEquiv_unitIso_inv_app_hom, Bimod.Hom.right_act_hom_assoc, CategoryTheory.CommMon.forget₂Mon_obj_X, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isModule, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_hom, monMonoidalStruct_tensorHom_hom, CategoryTheory.Grp.whiskerRight_hom, instIsIsoHomOfMapForget, braiding_hom_hom, CategoryTheory.Hom.mulEquivCongrRight_apply, equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, Bimod.AssociatorBimod.hom_right_act_hom', CategoryTheory.Mod_.trivialAction_mod_smul, CategoryTheory.Functor.id_mapMon_one, CategoryTheory.Grp.trivial_grp_mul, CategoryTheory.Comon.MonOpOpToComonObj_comon_counit, CategoryTheory.Bimon.toMonComonObj_X, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, tensorUnit_mul, uniqueHomToTrivial_default_hom, CategoryTheory.Bimon.equivMonComonCounitIsoApp_inv_hom_hom, tensor_one, hom_one, CategoryTheory.yonedaMon_obj, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, monMonoidalStruct_tensorObj_X, CategoryTheory.Functor.comp_mapMon_one, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_one, CategoryTheory.CommMon.forget₂Mon_obj_one, CategoryTheory.Grp.comp_hom, id_hom', CategoryTheory.Comon.ComonToMonOpOpObj_X, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_ε, snd_hom, Hom.hom_one, Bimod.LeftUnitorBimod.hom_left_act_hom', CategoryTheory.Comon.monoidal_tensorObj_comon_comul, tensor_mul, MonObj.mopEquiv_inverse_obj_mon_mul
comp 📖CompOp
1 mathmath: comp_hom
equivLaxMonoidalFunctorPUnit 📖CompOp
13 mathmath: equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, equivLaxMonoidalFunctorPUnit_functor_obj_X, equivLaxMonoidalFunctorPUnit_functor_obj_mon_mul, equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, equivLaxMonoidalFunctorPUnit_functor_map_hom, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, equivLaxMonoidalFunctorPUnit_inverse_obj_map, equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, equivLaxMonoidalFunctorPUnit_inverse_obj_obj, equivLaxMonoidalFunctorPUnit_functor_obj_mon_one, equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app
forget 📖CompOp
29 mathmath: forget_obj, forgetMapConeLimitConeIso_inv_hom, forget_μ, forget_ε, forgetMapConeLimitConeIso_hom_hom, CategoryTheory.Bimon.toMon_forget, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Bimon.toComon_obj_comon_counit, CategoryTheory.Bimon.toComon_map_hom, limitConeIsLimit_lift_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, forget_faithful, limit_mon_mul, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, instReflectsIsomorphismsForget, limitCone_π_app_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_X, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.Grp.forget₂Mon_comp_forget, limit_X, forget_η, CategoryTheory.CommMon.forget₂Mon_comp_forget, limit_mon_one, forget_δ, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, forget_map, instPreservesLimitsOfShapeForgetOfHasLimitsOfShape, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, CategoryTheory.Bimon.toComon_obj_comon_comul
homInhabited 📖CompOp
id 📖CompOp
1 mathmath: id_hom
instCategory 📖CompOp
395 mathmath: CategoryTheory.Grp.mkIso_inv_hom, CategoryTheory.Grp.Hom.hom_div, CategoryTheory.Grp.comp', CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_obj, CategoryTheory.Grp.mkIso_hom_hom, CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, CategoryTheory.Grp.instIsIsoHomHomMon, CategoryTheory.Grp.homMk'_hom, CategoryTheory.Bimon.toMonComonObj_mon_mul_hom, CategoryTheory.Functor.mapMonNatTrans_app_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, CategoryTheory.Functor.FullyFaithful.mapMon_preimage_hom, CategoryTheory.CommMon.comp_hom, CategoryTheory.Grp.Hom.hom_hom_zpow, CategoryTheory.Equivalence.mapMon_inverse, EquivLaxMonoidalFunctorPUnit.isMonHom_counitIsoAux, CategoryTheory.Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.Functor.mapCommMonNatIso_inv_app_hom_hom, forget_obj, CategoryTheory.instFullMonFunctorOppositeMonCatYonedaMon, forgetMapConeLimitConeIso_inv_hom, leftUnitor_inv_hom, CategoryTheory.Functor.mapCommMon_obj_mon_mul, forget_μ, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, CategoryTheory.Adjunction.mapMon_unit, CategoryTheory.Grp.id', CategoryTheory.Bimon.ext_iff, CategoryTheory.Comon.MonOpOpToComon_obj, CategoryTheory.CommMon.forget_map, CategoryTheory.Functor.FullyFaithful.mapGrp_preimage, CategoryTheory.Comon.ComonToMonOpOp_obj, CategoryTheory.Functor.mapMon_obj_mon_mul, CategoryTheory.CommGrp.mkIso_inv_hom, forget_ε, forgetMapConeLimitConeIso_hom_hom, CategoryTheory.shrinkYonedaMonObjObjEquiv_symm_comp, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, CategoryTheory.Grp.whiskerLeft_hom_hom, CategoryTheory.Functor.mapGrpIdIso_hom_app_hom_hom, CategoryTheory.Bimon.toMon_forget, CategoryTheory.Comon.Comon_EquivMon_OpOp_counitIso, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, CategoryTheory.instHasZeroObjectMon, CategoryTheory.Grp.leftUnitor_hom_hom, CategoryTheory.Functor.mapCommMonNatTrans_app_hom_hom, CategoryTheory.Comon.monoidal_rightUnitor_inv_hom, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, CategoryTheory.Bimon.trivial_comon_counit_hom, CategoryTheory.Bimon.toTrivial_hom, CategoryTheory.Bimon.instIsMonHomComonHomEquivMonComonCounitIsoAppX, CategoryTheory.Bimon.instIsComonHomHomEquivMonComonCounitIsoAppXAux, CategoryTheory.Bimon.equivMonComonUnitIsoApp_hom_hom_hom, rightUnitor_inv_hom, CategoryTheory.CommMon.mkIso'_inv_hom_hom, CategoryTheory.Grp.ε_def, CategoryTheory.Grp.rightUnitor_hom_hom_hom, CategoryTheory.Bimon.toComon_obj_comon_counit, mkIso_hom_hom, CategoryTheory.Bimon.toComon_map_hom, CategoryTheory.Grp.lift_hom, CategoryTheory.Grp.hom_mul, CategoryTheory.Bimon.trivial_X_X, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, CategoryTheory.Bimon.ofMonComonObj_comon_comul_hom, CategoryTheory.Monad.monadToMon_obj, equivLaxMonoidalFunctorPUnit_functor_obj_X, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_map_hom_app, CategoryTheory.Functor.mapMonCompIso_hom_app_hom, limitConeIsLimit_lift_hom, CategoryTheory.shrinkYonedaMon_map, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, CategoryTheory.Grp.Hom.hom_zpow, CategoryTheory.Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, CategoryTheory.Comon.Comon_EquivMon_OpOp_functor, CategoryTheory.Grp.ofHom_hom_hom, CategoryTheory.Bimon.toComon_obj_X, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, equivLaxMonoidalFunctorPUnit_functor_obj_mon_mul, CategoryTheory.Bimon.trivial_comon_comul_hom, CategoryTheory.Comon.MonOpOpToComon_map_hom, CategoryTheory.Grp.associator_inv_hom_hom, CategoryTheory.Monad.monToMonad_obj, CategoryTheory.Functor.mapCommMonNatIso_hom_app_hom_hom, MonObj.mopEquiv_functor_obj_mon_one_unmop, CategoryTheory.Grp.Hom.hom_hom_div, CategoryTheory.Grp.leftUnitor_hom_hom_hom, CategoryTheory.CommGrp.instIsIsoMonHomGrp, CategoryTheory.Grp.forget_map, CategoryTheory.Monoidal.monFunctorCategoryEquivalence_unitIso, tensorObj_one, lift_hom, whiskerRight_hom, CategoryTheory.Grp.mkIso_hom_hom_hom, CategoryTheory.CommMon.instIsIsoHomHomMon, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_inv, CategoryTheory.CommGrp.forget₂CommMon_map_hom, CategoryTheory.essImage_yonedaMon, CategoryTheory.Comon.ComonToMonOpOp_map, forget_faithful, CategoryTheory.Grp.rightUnitor_inv_hom_hom, CategoryTheory.Grp.forget₂Mon_map_hom, CategoryTheory.Comon.monoidal_whiskerLeft_hom, CategoryTheory.Equivalence.mapMon_unitIso, CategoryTheory.Monoidal.monFunctorCategoryEquivalence_functor, tensorUnit_X, CategoryTheory.instFaithfulMonFunctorOppositeMonCatYonedaMon, limit_mon_mul, CategoryTheory.Functor.mapMon_obj_X, CategoryTheory.Grp.whiskerRight_hom_hom, commBialgCatEquivComonCommAlgCat_functor_obj_unop_X, CategoryTheory.Functor.mapMonNatIso_hom_app_hom, CategoryTheory.Grp.Hom.hom_hom_inv, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, CategoryTheory.Comon.monoidal_leftUnitor_hom_hom, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, fst_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CategoryTheory.Grp.μ_def, CategoryTheory.Functor.mapMonNatIso_inv_app_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Grp.snd_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_obj, CategoryTheory.Monad.monadToMon_map_hom, mkIso_inv_hom, CategoryTheory.Grp.whiskerLeft_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.Adjunction.mapMon_counit, CategoryTheory.shrinkYonedaMon_obj, equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, CategoryTheory.Functor.mapMonFunctor_obj, CategoryTheory.Functor.mapGrpNatIso_hom_app_hom_hom, CategoryTheory.Bimon.instIsComonHomMonHomEquivMonComonUnitIsoAppX, CategoryTheory.Functor.mapCommMonCompIso_inv_app_hom_hom, CategoryTheory.Functor.comp_mapMon_mul, CategoryTheory.Functor.mapCommMonIdIso_hom_app_hom_hom, CategoryTheory.Grp.leftUnitor_inv_hom_hom, CategoryTheory.yonedaMon_map_app, instReflectsIsomorphismsForget, associator_hom_hom, ModuleCat.MonModuleEquivalenceAlgebra.functor_map_hom_apply, CategoryTheory.Functor.mapCommGrpNatIso_inv_app_hom_hom_hom, MonObj.mopEquiv_inverse_map_hom, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, comp_hom'_assoc, CategoryTheory.Bimon.BimonObjAux_counit, CategoryTheory.Grp.rightUnitor_inv_hom, ModuleCat.MonModuleEquivalenceAlgebra.functor_obj_carrier, CategoryTheory.Functor.mapMonFunctor_map_app_hom, CategoryTheory.Functor.mapMon_obj_mon_one, CategoryTheory.shrinkYonedaMon_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Functor.mapMonIdIso_hom_app_hom, CategoryTheory.Comon.monoidal_whiskerRight_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_map_hom_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_map_app_hom, CategoryTheory.CommGrp.hom_ext_iff, CategoryTheory.Grp.forget₂Mon_obj_mul, equivLaxMonoidalFunctorPUnit_functor_map_hom, MonObj.mopEquiv_inverse_obj_X, tensorObj_mul, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_map_hom_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, CategoryTheory.Grp.Hom.hom_pow, CategoryTheory.Grp.δ_def, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_counit, whiskerLeft_hom, CategoryTheory.Grp.associator_hom_hom_hom, CategoryTheory.CommMon.mkIso_inv_hom_hom, limitCone_π_app_hom, CategoryTheory.Grp.braiding_inv_hom, CategoryTheory.Grp.mkIso'_hom_hom_hom, CategoryTheory.Grp.id_hom, CategoryTheory.Comon.monoidal_associator_hom_hom, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, CategoryTheory.Functor.mapGrpCompIso_hom_app_hom_hom, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_obj, EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, CategoryTheory.Grp.fst_hom, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.instSmallCarrierObjOppositeMonCatMonFunctorYonedaMon, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_inv, CategoryTheory.CommGrp.mkIso_inv_hom_hom_hom, CategoryTheory.CommGrp.mkIso'_inv_hom_hom_hom, EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_mon, instIsCommMonObj, Hom.hom_mul, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_X, CategoryTheory.Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux, associator_inv_hom, CategoryTheory.CommMon.forget₂Mon_obj_mul, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_hom_hom, CategoryTheory.Monad.monToMonad_map_toNatTrans, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, equivLaxMonoidalFunctorPUnit_inverse_obj_map, mkIso'_inv_hom, uniqueHomFromTrivial_default_hom, CategoryTheory.Comon.Comon_EquivMon_OpOp_unitIso, EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, MonObj.mopEquiv_functor_map_hom_unmop, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObj_map_hom, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.Functor.mapCommMon_map_hom_hom, CategoryTheory.Functor.FullyFaithful.mapCommMon_preimage, CategoryTheory.Bimon.equivMonComonUnitIsoApp_inv_hom_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, CategoryTheory.Functor.mapGrp_map_hom_hom, CategoryTheory.CommGrp.forget₂Grp_map_hom, CategoryTheory.Grp.comp_hom_hom, CategoryTheory.Bimon.id_hom', CategoryTheory.Functor.mapMonIdIso_inv_app_hom, instIsCommMonObjOppositeCommAlgCatXUnopMonObjCommBialgCatFunctorCommBialgCatEquivComonCommAlgCatOfIsCocommCarrier, CategoryTheory.Bimon.trivialTo_hom, CategoryTheory.Equivalence.mapMon_counitIso, CategoryTheory.Bimon.ofMonComonObj_comon_counit_hom, MonObj.mopEquiv_unitIso_hom_app_hom, CategoryTheory.Grp.braiding_inv_hom_hom, CategoryTheory.Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.CommGrp.mkIso_hom_hom, instHasLimitsOfShape, CategoryTheory.Functor.mapCommMon_obj_mon_one, CategoryTheory.Bimon.ofMonComon_map_hom, CategoryTheory.Functor.Full.mapMon, tensorUnit_one, MonObj.mopEquiv_functor_obj_X_unmop, CategoryTheory.Grp.Hom.hom_mul, Hom.hom_pow, CategoryTheory.Grp.rightUnitor_hom_hom, CategoryTheory.Monad.monadMonEquiv_inverse, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.Bimon.ofMonComon_obj, CategoryTheory.Grp.forget₂Mon_obj_X, CategoryTheory.Grp.hom_ext_iff, CategoryTheory.instPreservesLimitsOfShapeMonFunctorOppositeMonCatShrinkYonedaMon, CategoryTheory.Grp.homMk''_hom_hom, equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, CategoryTheory.Comon.monoidal_tensorUnit_comon_comul, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, CategoryTheory.CommMon.id_hom, CategoryTheory.Grp.forget₂Mon_comp_forget, CategoryTheory.Bimon.toMonComon_obj, CategoryTheory.Functor.mapMon_map_hom, CategoryTheory.Functor.FullyFaithful.mapCommGrp_preimage, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_map, leftUnitor_hom_hom, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_inv_hom, CategoryTheory.Functor.mapGrpIdIso_inv_app_hom_hom, EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, CategoryTheory.Bimon.toMonComonObj_mon_one_hom, EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_map, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_mul, CategoryTheory.CommGrp.mkIso_hom_hom_hom_hom, CategoryTheory.CommMon.homMk_hom, CategoryTheory.Grp.leftUnitor_inv_hom, CategoryTheory.Functor.id_mapMon_mul, CategoryTheory.CommMon.mkIso_hom_hom_hom, CategoryTheory.Equivalence.mapMon_functor, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, MonObj.mopEquiv_functor_obj_mon_mul_unmop, equivLaxMonoidalFunctorPUnit_inverse_obj_obj, CategoryTheory.Bimon.BimonObjAux_comul, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isAddCommGroup, CategoryTheory.Functor.mapMonCompIso_inv_app_hom, limit_X, CategoryTheory.CommMon.hom_ext_iff, CategoryTheory.Grp.mkIso_inv_hom_hom, CategoryTheory.Bimon.equivMonComonCounitIsoApp_hom_hom_hom, CategoryTheory.Grp.snd_hom_hom, CategoryTheory.Functor.mapGrpNatTrans_app_hom_hom, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_comul, CategoryTheory.Comon.monoidal_leftUnitor_inv_hom, CategoryTheory.Monoidal.monFunctorCategoryEquivalence_counitIso, CategoryTheory.CommMon.instFullMonForget₂Mon, CategoryTheory.Grp.hom_one, CategoryTheory.Grp.forget₂Mon_obj_one, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, CategoryTheory.Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, comp_hom', CategoryTheory.Grp.associator_inv_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, braiding_inv_hom, CategoryTheory.Grp.homMk_hom_hom, CategoryTheory.Comon.monoidal_rightUnitor_hom_hom, CategoryTheory.Functor.essImage_mapMon, forget_η, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.Bimon.mk'_X, CategoryTheory.Functor.mapGrpNatIso_inv_app_hom_hom, commBialgCatEquivComonCommAlgCat_inverse_obj, hom_mul, limitCone_pt, CategoryTheory.Functor.mapGrpCompIso_inv_app_hom_hom, CategoryTheory.Grp.Hom.hom_inv, CategoryTheory.CommMon.forget₂Mon_comp_forget, limit_mon_one, CategoryTheory.Functor.mapCommGrpNatIso_hom_app_hom_hom_hom, MonObj.mopEquiv_inverse_obj_mon_one, CategoryTheory.Grp.instFaithfulMonForget₂Mon, CategoryTheory.Monad.monadMonEquiv_functor, forget_δ, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, rightUnitor_hom_hom, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_carrier, CategoryTheory.Bimon.ofMonComonObj_X, CategoryTheory.Grp.braiding_hom_hom, CategoryTheory.Functor.mapCommGrp_map_hom_hom_hom, CategoryTheory.Grp.η_def, CategoryTheory.Comon.monoidal_associator_inv_hom, CategoryTheory.Comon.Comon_EquivMon_OpOp_inverse, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, CategoryTheory.Bimon.toMonComon_map_hom, CategoryTheory.shrinkYonedaMon_obj_map_shrinkYonedaMonObjObjEquiv_symm, CategoryTheory.Grp.associator_hom_hom, CategoryTheory.Preadditive.commGrpEquivalence_inverse_map, forget_map, equivLaxMonoidalFunctorPUnit_functor_obj_mon_one, instPreservesLimitsOfShapeForgetOfHasLimitsOfShape, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, CategoryTheory.Functor.mapCommGrpNatTrans_app_hom_hom_hom, CategoryTheory.Functor.mapCommMonIdIso_inv_app_hom_hom, CategoryTheory.Comon.monoidal_tensorUnit_comon_counit, MonObj.mopEquiv_unitIso_inv_app_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.CommMon.forget₂Mon_obj_X, ModuleCat.MonModuleEquivalenceAlgebra.inverse_map_hom, CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isModule, EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_obj, CategoryTheory.yonedaGrp_map_app, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_hom, monMonoidalStruct_tensorHom_hom, CategoryTheory.CommGrp.mkIso'_hom_hom_hom_hom, CategoryTheory.Grp.whiskerRight_hom, braiding_hom_hom, CategoryTheory.Grp.tensorHom_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObj_obj, CategoryTheory.Hom.mulEquivCongrRight_apply, CategoryTheory.CommMon.mkIso'_hom_hom_hom, CategoryTheory.Grp.Hom.hom_one, CategoryTheory.CommMon.instFaithfulMonForget₂Mon, equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, CategoryTheory.Grp.fst_hom_hom, CategoryTheory.Grp.mkIso'_inv_hom_hom, CategoryTheory.Comon.monoidal_tensorHom_hom, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, CategoryTheory.Functor.id_mapMon_one, CategoryTheory.Bimon.trivial_X_mon_mul, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CategoryTheory.Preadditive.commGrpEquivalence_functor_map_hom_hom_hom, CategoryTheory.Bimon.comp_hom', CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, CategoryTheory.Grp.braiding_hom_hom_hom, tensorUnit_mul, uniqueHomToTrivial_default_hom, CategoryTheory.Bimon.equivMonComonCounitIsoApp_inv_hom_hom, CategoryTheory.CommMon.forget₂Mon_map_hom, tensor_one, hom_one, CategoryTheory.yonedaMon_obj, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, mkIso'_hom_hom, monMonoidalStruct_tensorObj_X, EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, CategoryTheory.Monoidal.monFunctorCategoryEquivalence_inverse, CategoryTheory.Functor.comp_mapMon_one, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_one, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_map_app_hom_hom, CategoryTheory.CommMon.forget₂Mon_obj_one, CategoryTheory.Grp.comp_hom, id_hom', CategoryTheory.Grp.instFullMonForget₂Mon, CategoryTheory.Grp.id_hom_hom, CategoryTheory.shrinkYonedaGrp_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Functor.Faithful.mapMon, CategoryTheory.Bimon.toComon_obj_comon_comul, snd_hom, equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, Hom.hom_one, CategoryTheory.CommGrp.forget_map, instHasInitial, CategoryTheory.Comon.monoidal_tensorObj_comon_comul, CategoryTheory.Bimon.trivial_X_mon_one, tensor_mul, CategoryTheory.Functor.mapCommMonCompIso_hom_app_hom_hom, MonObj.mopEquiv_inverse_obj_mon_mul
instInhabited 📖CompOp
instMonObjTensorObj 📖CompOp
14 mathmath: CategoryTheory.MonObj.instIsMonHomHomBraiding, CategoryTheory.BimonObj.one_comul, CategoryTheory.Functor.instIsMonHomμ, CategoryTheory.MonObj.instIsMonHomSnd, CategoryTheory.MonObj.instIsMonHomLift, CategoryTheory.MonObj.instIsMonHomFst, CategoryTheory.BimonObj.one_comul_assoc, CategoryTheory.Grp.tensorObj_mul, CategoryTheory.Grp.tensorObj_one, mul_def, CategoryTheory.MonObj.mul_braiding, CategoryTheory.instIsCommMonObjTensorObj, one_def, CategoryTheory.MonObj.instIsMonHomMulOfIsCommMonObj
instMonoidalForget 📖CompOp
5 mathmath: forget_μ, forget_ε, CategoryTheory.Bimon.toComon_map_hom, forget_η, forget_δ
instSymmetricCategory 📖CompOp
3 mathmath: instIsCommMonObj, braiding_inv_hom, braiding_hom_hom
mkIso 📖CompOp
2 mathmath: mkIso_hom_hom, mkIso_inv_hom
mkIso' 📖CompOp
4 mathmath: CategoryTheory.Hom.mulEquivCongrRight_symm_apply, mkIso'_inv_hom, CategoryTheory.Hom.mulEquivCongrRight_apply, mkIso'_hom_hom
mon 📖CompOp
118 mathmath: CategoryTheory.Bimon.toMonComonObj_mon_mul_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, CategoryTheory.Monad.ofMon_η, EquivLaxMonoidalFunctorPUnit.isMonHom_counitIsoAux, CategoryTheory.Bimon.ofMonComonObjX_mul, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.Functor.mapMon_obj_mon_mul, CategoryTheory.Over.monObjMkPullbackSnd_mul, CategoryTheory.shrinkYonedaMonObjObjEquiv_symm_comp, Bimod.TensorBimod.right_assoc', instIsMonHomHom, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, Bimod.actRight_one, CategoryTheory.Bimon.instIsMonHomComonHomEquivMonComonCounitIsoAppX, Bimod.left_assoc_assoc, Bimod.right_assoc, mkIso_hom_hom, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, Bimod.TensorBimod.actRight_one', CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, trivial_mon_mul, equivLaxMonoidalFunctorPUnit_functor_obj_mon_mul, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_one, MonObj.mopEquiv_functor_obj_mon_one_unmop, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_mul, tensorObj_one, limit_mon_mul, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, Bimod.right_assoc_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_obj, mkIso_inv_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.Functor.comp_mapMon_mul, CategoryTheory.yonedaMon_map_app, ModuleCat.MonModuleEquivalenceAlgebra.functor_map_hom_apply, MonObj.mopEquiv_inverse_map_hom, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, CategoryTheory.Monad.toMon_mon, CategoryTheory.Comon.MonOpOpToComonObj_comon_comul, CategoryTheory.Functor.mapMon_obj_mon_one, CategoryTheory.shrinkYonedaMon_map_app_shrinkYonedaObjObjEquiv_symm, Bimod.one_actLeft_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_map_app_hom, CategoryTheory.Grp.forget₂Mon_obj_mul, tensorObj_mul, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_mon, Hom.hom_mul, CategoryTheory.Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_μ, CategoryTheory.CommMon.forget₂Mon_obj_mul, CategoryTheory.Over.monObjMkPullbackSnd_one, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, uniqueHomFromTrivial_default_hom, MonObj.mopEquiv_functor_map_hom_unmop, AlgebraicGeometry.Scheme.monObjAsOverPullback_mul, Bimod.one_actLeft, instIsCommMonObjOppositeCommAlgCatXUnopMonObjCommBialgCatFunctorCommBialgCatEquivComonCommAlgCatOfIsCocommCarrier, Bimod.TensorBimod.left_assoc', trivial_mon_one, tensorUnit_one, Hom.hom_pow, Bimod.left_assoc, Bimod.regular_actRight, equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, CategoryTheory.Bimon.ofMonComonObjX_one, CategoryTheory.Functor.mapMon_map_hom, mul_def, CategoryTheory.Bimon.toMonComonObj_mon_one_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_mul, CategoryTheory.Functor.id_mapMon_mul, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, MonObj.mopEquiv_functor_obj_mon_mul_unmop, CategoryTheory.Monad.ofMon_μ, CategoryTheory.Bimon.equivMonComonCounitIsoApp_hom_hom_hom, CategoryTheory.Grp.forget₂Mon_obj_one, CategoryTheory.Mod_.trivialAction_X, Bimod.actRight_one_assoc, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.Comon.ComonToMonOpOpObj_mon_mul, commBialgCatEquivComonCommAlgCat_inverse_obj, hom_mul, Bimod.TensorBimod.one_act_left', limit_mon_one, MonObj.mopEquiv_inverse_obj_mon_one, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, CategoryTheory.shrinkYonedaMon_obj_map_shrinkYonedaMonObjObjEquiv_symm, one_def, equivLaxMonoidalFunctorPUnit_functor_obj_mon_one, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, Hom.isMonHom_hom, Bimod.regular_actLeft, AlgebraicGeometry.Scheme.monObjAsOverPullback_one, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, monMonoidalStruct_tensorHom_hom, CategoryTheory.Hom.mulEquivCongrRight_apply, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, CategoryTheory.Mod_.trivialAction_mod_smul, CategoryTheory.Functor.id_mapMon_one, CategoryTheory.Bimon.trivial_X_mon_mul, CategoryTheory.Comon.MonOpOpToComonObj_comon_counit, tensorUnit_mul, CategoryTheory.Bimon.equivMonComonCounitIsoApp_inv_hom_hom, tensor_one, hom_one, CategoryTheory.yonedaMon_obj, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Functor.comp_mapMon_one, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_one, CategoryTheory.CommMon.forget₂Mon_obj_one, EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_ε, Hom.hom_one, CategoryTheory.Comon.monoidal_tensorObj_comon_comul, CategoryTheory.Bimon.trivial_X_mon_one, tensor_mul, MonObj.mopEquiv_inverse_obj_mon_mul, CategoryTheory.Comon.ComonToMonOpOpObj_mon_one
monMonoidal 📖CompOp
58 mathmath: CategoryTheory.Bimon.toMonComonObj_mon_mul_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, forget_μ, CategoryTheory.Bimon.ext_iff, forget_ε, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_hom, CategoryTheory.Comon.monoidal_rightUnitor_inv_hom, CategoryTheory.Bimon.trivial_comon_counit_hom, CategoryTheory.Bimon.toTrivial_hom, CategoryTheory.Bimon.equivMonComonUnitIsoApp_hom_hom_hom, CategoryTheory.Grp.ε_def, CategoryTheory.Bimon.toComon_obj_comon_counit, CategoryTheory.Bimon.toComon_map_hom, CategoryTheory.Bimon.trivial_X_X, CategoryTheory.Bimon.ofMonComonObj_comon_comul_hom, CategoryTheory.Bimon.toComon_obj_X, CategoryTheory.Bimon.trivial_comon_comul_hom, CategoryTheory.Comon.monoidal_whiskerLeft_hom, CategoryTheory.Comon.monoidal_leftUnitor_hom_hom, CategoryTheory.Grp.μ_def, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.Bimon.instIsComonHomMonHomEquivMonComonUnitIsoAppX, CategoryTheory.Bimon.BimonObjAux_counit, CategoryTheory.Comon.monoidal_whiskerRight_hom, CategoryTheory.Grp.δ_def, CategoryTheory.Comon.monoidal_associator_hom_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_inv, instIsCommMonObj, CategoryTheory.Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux, CategoryTheory.Bimon.equivMonComonUnitIsoApp_inv_hom_hom, CategoryTheory.Bimon.id_hom', CategoryTheory.Bimon.trivialTo_hom, CategoryTheory.Bimon.ofMonComonObj_comon_counit_hom, CategoryTheory.Bimon.ofMonComon_map_hom, CategoryTheory.Comon.monoidal_tensorUnit_comon_comul, CategoryTheory.Bimon.toMonComonObj_mon_one_hom, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, CategoryTheory.Bimon.BimonObjAux_comul, CategoryTheory.Comon.monoidal_leftUnitor_inv_hom, braiding_inv_hom, CategoryTheory.Comon.monoidal_rightUnitor_hom_hom, forget_η, CategoryTheory.Bimon.mk'_X, hom_mul, forget_δ, CategoryTheory.Bimon.ofMonComonObj_X, CategoryTheory.Grp.η_def, CategoryTheory.Comon.monoidal_associator_inv_hom, CategoryTheory.Comon.monoidal_tensorUnit_comon_counit, braiding_hom_hom, CategoryTheory.Comon.monoidal_tensorHom_hom, CategoryTheory.Bimon.trivial_X_mon_mul, CategoryTheory.Bimon.comp_hom', hom_one, CategoryTheory.Bimon.toComon_obj_comon_comul, CategoryTheory.Comon.monoidal_tensorObj_comon_comul, CategoryTheory.Bimon.trivial_X_mon_one
monMonoidalStruct 📖CompOp
18 mathmath: leftUnitor_inv_hom, rightUnitor_inv_hom, tensorObj_one, whiskerRight_hom, tensorUnit_X, associator_hom_hom, tensorObj_mul, whiskerLeft_hom, associator_inv_hom, tensorUnit_one, leftUnitor_hom_hom, rightUnitor_hom_hom, monMonoidalStruct_tensorHom_hom, CategoryTheory.Grp.tensorHom_hom, tensorUnit_mul, tensor_one, monMonoidalStruct_tensorObj_X, tensor_mul
trivial 📖CompOp
14 mathmath: CategoryTheory.Grp.trivial_grp_inv, trivial_mon_mul, equivLaxMonoidalFunctorPUnit_functor_obj_mon_mul, equivLaxMonoidalFunctorPUnit_functor_map_hom, uniqueHomFromTrivial_default_hom, CategoryTheory.Bimon.trivialTo_hom, trivial_mon_one, EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_map, CategoryTheory.Grp.trivial_grp_one, trivial_X, equivLaxMonoidalFunctorPUnit_functor_obj_mon_one, EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_obj, CategoryTheory.Grp.trivial_grp_mul, uniqueHomToTrivial_default_hom
uniqueHomFromTrivial 📖CompOp
2 mathmath: uniqueHomFromTrivial_default_hom, CategoryTheory.Bimon.trivialTo_hom

Theorems

NameKindAssumesProvesValidatesDepends On
associator_hom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
associator_inv_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
braiding_hom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
monMonoidal
CategoryTheory.SymmetricCategory.toBraidedCategory
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
instSymmetricCategory
X
braiding_inv_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
monMonoidal
CategoryTheory.SymmetricCategory.toBraidedCategory
CategoryTheory.Iso.inv
CategoryTheory.BraidedCategory.braiding
instSymmetricCategory
X
comp_hom 📖mathematicalHom.hom
comp
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
X
comp_hom' 📖mathematicalHom.hom
CategoryTheory.CategoryStruct.comp
CategoryTheory.Mon
CategoryTheory.Category.toCategoryStruct
instCategory
X
comp_hom'_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
X
Hom.hom
CategoryTheory.Mon
instCategory
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_hom'
equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom 📖mathematicalHom.hom
CategoryTheory.Functor.obj
CategoryTheory.Mon
instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal
EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon
CategoryTheory.Functor.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.counitIso
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
X
equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom 📖mathematicalHom.hom
CategoryTheory.Functor.obj
CategoryTheory.Mon
instCategory
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal
EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.counitIso
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
X
equivLaxMonoidalFunctorPUnit_functor_map_hom 📖mathematicalHom.hom
CategoryTheory.Functor.obj
CategoryTheory.Mon
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.mapMonFunctor
trivial
CategoryTheory.Functor.map
CategoryTheory.Equivalence.functor
equivLaxMonoidalFunctorPUnit
CategoryTheory.NatTrans.app
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
equivLaxMonoidalFunctorPUnit_functor_obj_X 📖mathematicalX
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Mon
instCategory
CategoryTheory.Equivalence.functor
equivLaxMonoidalFunctorPUnit
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
equivLaxMonoidalFunctorPUnit_functor_obj_mon_mul 📖mathematicalCategoryTheory.MonObj.mul
CategoryTheory.Functor.obj
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
X
trivial
mon
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Mon
instCategory
CategoryTheory.Equivalence.functor
equivLaxMonoidalFunctorPUnit
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Discrete.functor_map_id
CategoryTheory.Category.comp_id
equivLaxMonoidalFunctorPUnit_functor_obj_mon_one 📖mathematicalCategoryTheory.MonObj.one
CategoryTheory.Functor.obj
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
X
trivial
mon
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Mon
instCategory
CategoryTheory.Equivalence.functor
equivLaxMonoidalFunctorPUnit
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.Discrete.functor_map_id
CategoryTheory.Category.comp_id
equivLaxMonoidalFunctorPUnit_inverse_map_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.of
EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj
EquivLaxMonoidalFunctorPUnit.instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Functor.map
CategoryTheory.Mon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
Hom.hom
equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε 📖mathematicalCategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.Functor.obj
CategoryTheory.Mon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
CategoryTheory.MonObj.one
X
mon
equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ 📖mathematicalCategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.Functor.obj
CategoryTheory.Mon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
CategoryTheory.MonObj.mul
X
mon
equivLaxMonoidalFunctorPUnit_inverse_obj_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.Mon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
X
equivLaxMonoidalFunctorPUnit_inverse_obj_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Mon
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Equivalence.inverse
equivLaxMonoidalFunctorPUnit
X
equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.Mon
instCategory
EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon
EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.unitIso
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Discrete.functor_map_id
equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor.comp
CategoryTheory.Mon
instCategory
EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon
EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal
CategoryTheory.Functor.id
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Equivalence.unitIso
equivLaxMonoidalFunctorPUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Discrete.functor_map_id
forget_faithful 📖mathematicalCategoryTheory.Functor.Faithful
CategoryTheory.Mon
instCategory
forget
Hom.ext'
forget_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Mon
instCategory
forget
Hom.hom
forget_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Mon
instCategory
forget
X
forget_δ 📖mathematicalCategoryTheory.Functor.OplaxMonoidal.δ
CategoryTheory.Mon
instCategory
monMonoidal
forget
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
instMonoidalForget
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
forget_ε 📖mathematicalCategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Mon
instCategory
monMonoidal
forget
CategoryTheory.Functor.Monoidal.toLaxMonoidal
instMonoidalForget
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
forget_η 📖mathematicalCategoryTheory.Functor.OplaxMonoidal.η
CategoryTheory.Mon
instCategory
monMonoidal
forget
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
instMonoidalForget
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
forget_μ 📖mathematicalCategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Mon
instCategory
monMonoidal
forget
CategoryTheory.Functor.Monoidal.toLaxMonoidal
instMonoidalForget
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
hom_injective 📖mathematicalHom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
X
Hom.hom
Hom.ext
id_hom 📖mathematicalHom.hom
id
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
X
id_hom' 📖mathematicalHom.hom
CategoryTheory.CategoryStruct.id
CategoryTheory.Mon
CategoryTheory.Category.toCategoryStruct
instCategory
X
instHasInitial 📖mathematicalCategoryTheory.Limits.HasInitial
CategoryTheory.Mon
instCategory
CategoryTheory.Limits.hasInitial_of_unique
Unique.instSubsingleton
instIsIsoHom 📖mathematicalCategoryTheory.IsIso
X
Hom.hom
instIsIsoHomOfMapForget 📖mathematicalCategoryTheory.IsIso
X
Hom.hom
instIsMonHomHom 📖mathematicalCategoryTheory.IsMonHom
X
mon
Hom.hom
Hom.isMonHom_hom
instReflectsIsomorphismsForget 📖mathematicalCategoryTheory.Functor.ReflectsIsomorphisms
CategoryTheory.Mon
instCategory
forget
instIsIsoHomOfMapForget
CategoryTheory.IsMonHom.one_hom
instIsMonHomHom
CategoryTheory.Category.assoc
CategoryTheory.IsMonHom.mul_hom
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc
CategoryTheory.IsIso.inv_hom_id
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.Category.id_comp
Hom.ext'
CategoryTheory.IsIso.hom_inv_id
leftUnitor_hom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
leftUnitor_inv_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
mkIso'_hom_hom 📖mathematicalHom.hom
CategoryTheory.Iso.hom
CategoryTheory.Mon
instCategory
mkIso'
mkIso'_inv_hom 📖mathematicalHom.hom
CategoryTheory.Iso.inv
CategoryTheory.Mon
instCategory
mkIso'
mkIso_hom_hom 📖mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
CategoryTheory.CategoryStruct.comp
CategoryTheory.MonObj.one
mon
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategoryStruct.tensorHom
Hom.hom
X
mon
CategoryTheory.Iso.hom
CategoryTheory.Mon
instCategory
mkIso
mkIso_inv_hom 📖mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
CategoryTheory.CategoryStruct.comp
CategoryTheory.MonObj.one
mon
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategoryStruct.tensorHom
Hom.hom
X
mon
CategoryTheory.Iso.inv
CategoryTheory.Mon
instCategory
mkIso
monMonoidalStruct_tensorHom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
CategoryTheory.MonObj.tensorObj.instTensorObj
mon
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Mon
instCategory
monMonoidalStruct
monMonoidalStruct_tensorObj_X 📖mathematicalX
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
mul_def 📖mathematicalCategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instMonObjTensorObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
mon
one_def 📖mathematicalCategoryTheory.MonObj.one
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instMonObjTensorObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
mon
rightUnitor_hom_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
rightUnitor_inv_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
tensorObj_mul 📖mathematicalCategoryTheory.MonObj.mul
X
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensorObj_one 📖mathematicalCategoryTheory.MonObj.one
X
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensorUnit_X 📖mathematicalX
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorUnit_mul 📖mathematicalCategoryTheory.MonObj.mul
X
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Mon
instCategory
monMonoidalStruct
mon
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.leftUnitor
tensorUnit_one 📖mathematicalCategoryTheory.MonObj.one
X
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Mon
instCategory
monMonoidalStruct
mon
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensor_mul 📖mathematicalCategoryTheory.MonObj.mul
X
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensor_one 📖mathematicalCategoryTheory.MonObj.one
X
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
trivial_X 📖mathematicalX
trivial
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
trivial_mon_mul 📖mathematicalCategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
mon
trivial
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategoryStruct.leftUnitor
trivial_mon_one 📖mathematicalCategoryTheory.MonObj.one
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
mon
trivial
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
uniqueHomFromTrivial_default_hom 📖mathematicalHom.hom
trivial
Quiver.Hom
CategoryTheory.Mon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
instCategory
Unique.toInhabited
uniqueHomFromTrivial
CategoryTheory.MonObj.one
X
mon
whiskerLeft_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X
whiskerRight_hom 📖mathematicalHom.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
monMonoidalStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
X

CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit

Definitions

NameCategoryTheorems
counitIso 📖CompOp
2 mathmath: counitIso_inv_app_hom, counitIso_hom_app_hom
counitIsoAux 📖CompOp
3 mathmath: isMonHom_counitIsoAux, counitIsoAux_inv, counitIsoAux_hom
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj 📖CompOp
5 mathmath: monToLaxMonoidal_map_hom_app, monToLaxMonoidal_obj, monToLaxMonoidalObj_μ, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, monToLaxMonoidalObj_ε
laxMonoidalToMon 📖CompOp
15 mathmath: isMonHom_counitIsoAux, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, monToLaxMonoidal_laxMonoidalToMon_obj_one, unitIso_hom_app_hom_app, counitIso_inv_app_hom, counitIsoAux_inv, counitIso_hom_app_hom, counitIsoAux_hom, laxMonoidalToMon_map, monToLaxMonoidal_laxMonoidalToMon_obj_mul, laxMonoidalToMon_obj, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, unitIso_inv_app_hom_app, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app
monToLaxMonoidal 📖CompOp
15 mathmath: isMonHom_counitIsoAux, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, monToLaxMonoidal_map_hom_app, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, monToLaxMonoidal_laxMonoidalToMon_obj_one, monToLaxMonoidal_obj, unitIso_hom_app_hom_app, counitIso_inv_app_hom, counitIsoAux_inv, counitIso_hom_app_hom, counitIsoAux_hom, monToLaxMonoidal_laxMonoidalToMon_obj_mul, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, unitIso_inv_app_hom_app, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app
monToLaxMonoidalObj 📖CompOp
9 mathmath: monToLaxMonoidal_map_hom_app, monToLaxMonoidalObj_obj, monToLaxMonoidal_obj, monToLaxMonoidalObj_map, monToLaxMonoidalObj_μ, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, monToLaxMonoidalObj_ε
unitIso 📖CompOp
2 mathmath: unitIso_hom_app_hom_app, unitIso_inv_app_hom_app

Theorems

NameKindAssumesProvesValidatesDepends On
counitIsoAux_hom 📖mathematicalCategoryTheory.Iso.hom
CategoryTheory.Mon.X
CategoryTheory.Functor.obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
monToLaxMonoidal
laxMonoidalToMon
CategoryTheory.Functor.id
counitIsoAux
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
counitIsoAux_inv 📖mathematicalCategoryTheory.Iso.inv
CategoryTheory.Mon.X
CategoryTheory.Functor.obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
monToLaxMonoidal
laxMonoidalToMon
CategoryTheory.Functor.id
counitIsoAux
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
counitIso_hom_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
CategoryTheory.Functor.obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
monToLaxMonoidal
laxMonoidalToMon
CategoryTheory.Functor.id
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
counitIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.X
counitIso_inv_app_hom 📖mathematicalCategoryTheory.Mon.Hom.hom
CategoryTheory.Functor.obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
monToLaxMonoidal
laxMonoidalToMon
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
counitIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.X
isMonHom_counitIsoAux 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.Mon.X
CategoryTheory.Functor.obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
monToLaxMonoidal
laxMonoidalToMon
CategoryTheory.Functor.id
CategoryTheory.Mon.mon
CategoryTheory.Iso.hom
counitIsoAux
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.Category.id_comp
laxMonoidalToMon_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
laxMonoidalToMon
CategoryTheory.NatTrans.app
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.mapMonFunctor
CategoryTheory.Mon.trivial
laxMonoidalToMon_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
laxMonoidalToMon
CategoryTheory.Functor.mapMon
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.LaxMonoidalFunctor.laxMonoidal
CategoryTheory.Mon.trivial
monToLaxMonoidalObj_map 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.Discrete
CategoryTheory.discreteCategory
monToLaxMonoidalObj
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.X
monToLaxMonoidalObj_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Discrete
CategoryTheory.discreteCategory
monToLaxMonoidalObj
CategoryTheory.Mon.X
monToLaxMonoidalObj_ε 📖mathematicalCategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
monToLaxMonoidalObj
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
CategoryTheory.MonObj.one
CategoryTheory.Mon.X
CategoryTheory.Mon.mon
monToLaxMonoidalObj_μ 📖mathematicalCategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
monToLaxMonoidalObj
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
CategoryTheory.MonObj.mul
CategoryTheory.Mon.X
CategoryTheory.Mon.mon
monToLaxMonoidal_laxMonoidalToMon_obj_mul 📖mathematicalCategoryTheory.MonObj.mul
CategoryTheory.Mon.X
CategoryTheory.Functor.obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
monToLaxMonoidal
laxMonoidalToMon
CategoryTheory.Mon.mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.id
monToLaxMonoidal_laxMonoidalToMon_obj_one 📖mathematicalCategoryTheory.MonObj.one
CategoryTheory.Mon.X
CategoryTheory.Functor.obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.Functor.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
monToLaxMonoidal
laxMonoidalToMon
CategoryTheory.Mon.mon
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.CategoryStruct.id
monToLaxMonoidal_map_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.of
monToLaxMonoidalObj
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Functor.map
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
monToLaxMonoidal
CategoryTheory.Mon.Hom.hom
monToLaxMonoidal_obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.LaxMonoidalFunctor.instCategory
monToLaxMonoidal
CategoryTheory.LaxMonoidalFunctor.of
monToLaxMonoidalObj
instLaxMonoidalDiscretePUnitMonToLaxMonoidalObj
unitIso_hom_app_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
laxMonoidalToMon
monToLaxMonoidal
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
unitIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Discrete.functor_map_id
unitIso_inv_app_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.LaxMonoidalFunctor.toFunctor
CategoryTheory.Discrete.addMonoidal
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
CategoryTheory.Functor.obj
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Functor.comp
CategoryTheory.Mon
CategoryTheory.Mon.instCategory
laxMonoidalToMon
monToLaxMonoidal
CategoryTheory.Functor.id
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
unitIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Discrete.functor_map_id

CategoryTheory.Mon.Hom

Definitions

NameCategoryTheorems
hom 📖CompOp
217 mathmath: CategoryTheory.Grp.mkIso_inv_hom, CategoryTheory.Grp.Hom.hom_div, CategoryTheory.Grp.mkIso_hom_hom, CategoryTheory.Mon.id_hom, CategoryTheory.Grp.instIsIsoHomHomMon, CategoryTheory.Functor.mapMonNatTrans_app_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, CategoryTheory.Functor.FullyFaithful.mapMon_preimage_hom, CategoryTheory.CommMon.comp_hom, CategoryTheory.Grp.Hom.hom_hom_zpow, CategoryTheory.Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.Functor.mapCommMonNatIso_inv_app_hom_hom, CategoryTheory.Mon.leftUnitor_inv_hom, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, CategoryTheory.Bimon.ext_iff, CategoryTheory.CommMon.forget_map, CategoryTheory.Mon.hom_injective, CategoryTheory.CommGrp.mkIso_inv_hom, CategoryTheory.Mon.instIsMonHomHom, CategoryTheory.Grp.whiskerLeft_hom_hom, CategoryTheory.Functor.mapGrpIdIso_hom_app_hom_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, CategoryTheory.Grp.leftUnitor_hom_hom, CategoryTheory.Functor.mapCommMonNatTrans_app_hom_hom, CategoryTheory.Comon.monoidal_rightUnitor_inv_hom, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, CategoryTheory.Bimon.trivial_comon_counit_hom, CategoryTheory.Bimon.equivMonComonUnitIsoApp_hom_hom_hom, CategoryTheory.Mon.rightUnitor_inv_hom, CategoryTheory.CommMon.mkIso'_inv_hom_hom, CategoryTheory.Grp.rightUnitor_hom_hom_hom, CategoryTheory.Bimon.toComon_obj_comon_counit, CategoryTheory.Mon.mkIso_hom_hom, CategoryTheory.Bimon.toComon_map_hom, CategoryTheory.Grp.hom_mul, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, CategoryTheory.Bimon.ofMonComonObj_comon_comul_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_map_hom_app, CategoryTheory.Functor.mapMonCompIso_hom_app_hom, CategoryTheory.Mon.limitConeIsLimit_lift_hom, CategoryTheory.Grp.Hom.hom_zpow, CategoryTheory.Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, CategoryTheory.Grp.ofHom_hom_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, CategoryTheory.Bimon.trivial_comon_comul_hom, CategoryTheory.Comon.MonOpOpToComon_map_hom, CategoryTheory.Grp.associator_inv_hom_hom, CategoryTheory.Functor.mapCommMonNatIso_hom_app_hom_hom, CategoryTheory.Grp.Hom.hom_hom_div, CategoryTheory.Grp.leftUnitor_hom_hom_hom, CategoryTheory.Grp.forget_map, CategoryTheory.Mon.lift_hom, CategoryTheory.Mon.whiskerRight_hom, CategoryTheory.Grp.mkIso_hom_hom_hom, CategoryTheory.CommMon.instIsIsoHomHomMon, CategoryTheory.Grp.rightUnitor_inv_hom_hom, CategoryTheory.Grp.forget₂Mon_map_hom, CategoryTheory.Grp.whiskerRight_hom_hom, CategoryTheory.Functor.mapMonNatIso_hom_app_hom, CategoryTheory.Grp.Hom.hom_hom_inv, CategoryTheory.Comon.monoidal_leftUnitor_hom_hom, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, ext'_iff, CategoryTheory.Mon.fst_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CategoryTheory.Functor.mapMonNatIso_inv_app_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Grp.snd_hom, CategoryTheory.Monad.monadToMon_map_hom, CategoryTheory.Mon.mkIso_inv_hom, CategoryTheory.Grp.whiskerLeft_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.Functor.mapGrpNatIso_hom_app_hom_hom, CategoryTheory.Functor.mapCommMonCompIso_inv_app_hom_hom, CategoryTheory.Functor.mapCommMonIdIso_hom_app_hom_hom, CategoryTheory.Grp.leftUnitor_inv_hom_hom, CategoryTheory.yonedaMon_map_app, CategoryTheory.Mon.associator_hom_hom, ModuleCat.MonModuleEquivalenceAlgebra.functor_map_hom_apply, CategoryTheory.Functor.mapCommGrpNatIso_inv_app_hom_hom_hom, MonObj.mopEquiv_inverse_map_hom, CategoryTheory.Mon.comp_hom'_assoc, CategoryTheory.Bimon.BimonObjAux_counit, CategoryTheory.Grp.rightUnitor_inv_hom, CategoryTheory.Functor.mapMonFunctor_map_app_hom, CategoryTheory.shrinkYonedaMon_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Functor.mapMonIdIso_hom_app_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_map_hom_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_map_app_hom, CategoryTheory.CommGrp.hom_ext_iff, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_functor_map_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_map_hom_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, CategoryTheory.Mon.whiskerLeft_hom, CategoryTheory.Grp.associator_hom_hom_hom, CategoryTheory.CommMon.mkIso_inv_hom_hom, CategoryTheory.Mon.limitCone_π_app_hom, CategoryTheory.Grp.braiding_inv_hom, CategoryTheory.Grp.mkIso'_hom_hom_hom, CategoryTheory.Grp.id_hom, CategoryTheory.Comon.monoidal_associator_hom_hom, CategoryTheory.Functor.mapGrpCompIso_hom_app_hom_hom, CategoryTheory.Grp.fst_hom, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.CommGrp.mkIso_inv_hom_hom_hom, CategoryTheory.CommGrp.mkIso'_inv_hom_hom_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, hom_mul, CategoryTheory.Mon.associator_inv_hom, CategoryTheory.Monad.monToMonad_map_toNatTrans, CategoryTheory.Mon.mkIso'_inv_hom, CategoryTheory.Mon.uniqueHomFromTrivial_default_hom, MonObj.mopEquiv_functor_map_hom_unmop, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObj_map_hom, ext_iff, CategoryTheory.Functor.mapCommMon_map_hom_hom, CategoryTheory.Bimon.equivMonComonUnitIsoApp_inv_hom_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, CategoryTheory.Functor.mapGrp_map_hom_hom, CategoryTheory.Grp.comp_hom_hom, CategoryTheory.Functor.mapMonIdIso_inv_app_hom, CategoryTheory.Bimon.ofMonComonObj_comon_counit_hom, MonObj.mopEquiv_unitIso_hom_app_hom, CategoryTheory.Grp.braiding_inv_hom_hom, CategoryTheory.Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.CommGrp.mkIso_hom_hom, hom_pow, CategoryTheory.Grp.rightUnitor_hom_hom, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.Grp.hom_ext_iff, CategoryTheory.Grp.homMk''_hom_hom, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_inverse_map_hom_app, CategoryTheory.CommMon.id_hom, CategoryTheory.Functor.mapMon_map_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_map, CategoryTheory.Mon.leftUnitor_hom_hom, CategoryTheory.Functor.mapGrpIdIso_inv_app_hom_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, CategoryTheory.CommGrp.mkIso_hom_hom_hom_hom, CategoryTheory.Grp.leftUnitor_inv_hom, CategoryTheory.CommMon.mkIso_hom_hom_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, CategoryTheory.Bimon.BimonObjAux_comul, CategoryTheory.Functor.mapMonCompIso_inv_app_hom, CategoryTheory.CommMon.hom_ext_iff, CategoryTheory.Grp.mkIso_inv_hom_hom, CategoryTheory.Bimon.equivMonComonCounitIsoApp_hom_hom_hom, CategoryTheory.Grp.snd_hom_hom, CategoryTheory.Functor.mapGrpNatTrans_app_hom_hom, CategoryTheory.Comon.monoidal_leftUnitor_inv_hom, CategoryTheory.Grp.hom_one, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, CategoryTheory.Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, CategoryTheory.Mon.comp_hom', CategoryTheory.Grp.associator_inv_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Mon.braiding_inv_hom, CategoryTheory.Grp.homMk_hom_hom, CategoryTheory.Comon.monoidal_rightUnitor_hom_hom, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.Functor.mapGrpNatIso_inv_app_hom_hom, CategoryTheory.Mon.hom_mul, CategoryTheory.Mon.comp_hom, CategoryTheory.Functor.mapGrpCompIso_inv_app_hom_hom, CategoryTheory.Grp.Hom.hom_inv, CategoryTheory.Functor.mapCommGrpNatIso_hom_app_hom_hom_hom, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, CategoryTheory.Mon.rightUnitor_hom_hom, CategoryTheory.Grp.braiding_hom_hom, CategoryTheory.Functor.mapCommGrp_map_hom_hom_hom, CategoryTheory.Comon.monoidal_associator_inv_hom, CategoryTheory.Bimon.toMonComon_map_hom, CategoryTheory.Grp.associator_hom_hom, CategoryTheory.Preadditive.commGrpEquivalence_inverse_map, CategoryTheory.Mon.forget_map, CategoryTheory.Mon.instIsIsoHom, CategoryTheory.Functor.mapCommGrpNatTrans_app_hom_hom_hom, CategoryTheory.Functor.mapCommMonIdIso_inv_app_hom_hom, isMonHom_hom, MonObj.mopEquiv_unitIso_inv_app_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, ModuleCat.MonModuleEquivalenceAlgebra.inverse_map_hom, CategoryTheory.Mon.monMonoidalStruct_tensorHom_hom, CategoryTheory.CommGrp.mkIso'_hom_hom_hom_hom, CategoryTheory.Grp.whiskerRight_hom, CategoryTheory.Mon.instIsIsoHomOfMapForget, CategoryTheory.Mon.braiding_hom_hom, CategoryTheory.CommMon.mkIso'_hom_hom_hom, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, CategoryTheory.Grp.fst_hom_hom, CategoryTheory.Grp.mkIso'_inv_hom_hom, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CategoryTheory.Preadditive.commGrpEquivalence_functor_map_hom_hom_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, CategoryTheory.Grp.braiding_hom_hom_hom, CategoryTheory.Mon.uniqueHomToTrivial_default_hom, CategoryTheory.Bimon.equivMonComonCounitIsoApp_inv_hom_hom, CategoryTheory.CommMon.forget₂Mon_map_hom, CategoryTheory.Mon.hom_one, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Mon.mkIso'_hom_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_map_app_hom_hom, CategoryTheory.Grp.comp_hom, CategoryTheory.Mon.id_hom', CategoryTheory.Grp.id_hom_hom, CategoryTheory.shrinkYonedaGrp_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Bimon.toComon_obj_comon_comul, CategoryTheory.Mon.snd_hom, hom_one, CategoryTheory.CommGrp.forget_map, CategoryTheory.Functor.mapCommMonCompIso_hom_app_hom_hom
mk' 📖CompOp
5 mathmath: commBialgCatEquivComonCommAlgCat_unitIso_inv_app, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, CategoryTheory.Functor.mapCommMonFunctor_map_app, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, commBialgCatEquivComonCommAlgCat_counitIso_inv_app

Theorems

NameKindAssumesProvesValidatesDepends On
ext 📖hom
ext' 📖homext
ext'_iff 📖mathematicalhomext'
ext_iff 📖mathematicalhomext
isMonHom_hom 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.Mon.X
CategoryTheory.Mon.mon
hom

CategoryTheory.MonObj

Definitions

NameCategoryTheorems
instTensorUnit 📖CompOp
11 mathmath: CategoryTheory.IsCommMonObj.instTensorUnit, instIsMonHomOne, instIsMonHomToUnit, mul_def, one_def, instIsMonHomHomLeftUnitor, CategoryTheory.Grp.tensorUnit_mul, CategoryTheory.Grp.tensorUnit_one, instIsMonHomHomRightUnitor, CategoryTheory.Functor.instIsMonHomε, CategoryTheory.ModObj.smul_def
mul 📖CompOp
176 mathmath: CategoryTheory.GrpObj.lift_inv_comp_left, CategoryTheory.Bimon.toMonComonObj_mon_mul_hom, CategoryTheory.Functor.mapCommMon_obj_mon_mul, CategoryTheory.ModObj.mul_smul_assoc, CategoryTheory.Bimon.ofMonComonObjX_mul, CategoryTheory.Monad.mul_def, CategoryTheory.GrpObj.lift_inv_right_eq, mul_assoc, CategoryTheory.GrpObj.lift_inv_comp_left_assoc, ofIso_mul, CategoryTheory.Functor.mapMon_obj_mon_mul, CategoryTheory.Over.monObjMkPullbackSnd_mul, CategoryTheory.Functor.comp_mapGrp_mul, Bimod.TensorBimod.right_assoc', CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul, CategoryTheory.GrpObj.left_inv_assoc, CategoryTheory.Functor.mapGrp_id_mul, CategoryTheory.Over.grpObjMkPullbackSnd_mul, CategoryTheory.Functor.FullyFaithful.monObj_mul, lift_comp_one_right, Bimod.left_assoc_assoc, Bimod.right_assoc, CategoryTheory.GrpObj.lift_inv_comp_right, CategoryTheory.HopfObj.mul_antipode, CategoryTheory.Grp.hom_mul, lift_lift_assoc, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_mul, mul_leftUnitor, lift_comp_one_right_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, CategoryTheory.Bimon.compatibility_assoc, CategoryTheory.ModObj.mul_smul'_assoc, CategoryTheory.BimonObj.mul_counit_assoc, CategoryTheory.Mon.trivial_mon_mul, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_functor_obj_mon_mul, CategoryTheory.GrpObj.lift_comp_inv_right_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_mul, CategoryTheory.CommGrp.forget₂Grp_obj_mul, mul_def, mul_mul_mul_comm'_assoc, one_mul_assoc, CategoryTheory.HopfObj.antipode_left, CategoryTheory.GrpObj.tensorHom_inv_inv_mul_assoc, CategoryTheory.Mon.limit_mon_mul, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom, ext_iff, CommAlgCat.mul_op_of_unop_hom, mul_mul_mul_comm, CategoryTheory.Hom.mul_def, Bimod.right_assoc_assoc, tensorObj.mul_def, lift_comp_one_left, CategoryTheory.Grp.tensorUnit_mul, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv, CategoryTheory.Functor.comp_mapMon_mul, CategoryTheory.HopfObj.antipode_comul₂, CategoryTheory.IsMonHom.mul_hom, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul_assoc, CategoryTheory.BimonObj.mul_comul_assoc, CategoryTheory.Functor.comp_mapCommMon_mul, CategoryTheory.Comon.MonOpOpToComonObj_comon_comul, CategoryTheory.HopfObj.antipode_left_assoc, CategoryTheory.ModObj.smul_eq_mul, mul_one, CategoryTheory.Grp.forget₂Mon_obj_mul, CategoryTheory.Mon.tensorObj_mul, CategoryTheory.GrpObj.lift_inv_left_eq, CategoryTheory.Functor.comp_mapCommGrp_mul, Mon_tensor_mul_one, CategoryTheory.BimonObj.mul_counit, Mon_tensor_one_mul, CategoryTheory.Functor.mapCommMon_id_mul, CategoryTheory.Mathlib.Tactic.MonTauto.eq_mul_one, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_μ, CategoryTheory.CommMon.forget₂Mon_obj_mul, CategoryTheory.Conv.mul_eq, CategoryTheory.GrpObj.isPullback, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_μ, CategoryTheory.Functor.obj.μ_def, AlgebraicGeometry.Scheme.monObjAsOverPullback_mul, Mon_tensor_mul_assoc, CategoryTheory.IsCommMonObj.mul_comm'_assoc, mul_mul_mul_comm', CategoryTheory.HopfObj.mul_antipode₁, CategoryTheory.CommGrp.forget₂CommMon_obj_mul, Bimod.TensorBimod.left_assoc', CategoryTheory.GrpObj.eq_lift_inv_right, mul_mul_mul_comm_assoc, ModuleCat.MonModuleEquivalenceAlgebra.inverseObj_mul, ofRepresentableBy_mul, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj_μ, CategoryTheory.GrpObj.left_inv, CategoryTheory.Bimon.mul_counit, CategoryTheory.ModObj.assoc_flip, CategoryTheory.HopfObj.antipode_right_assoc, CategoryTheory.GrpObj.mul_inv_rev_assoc, CategoryTheory.Grp.tensorObj_mul, Bimod.left_assoc, Bimod.regular_actRight, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul, CategoryTheory.GrpObj.tensorHom_inv_inv_mul, mul_associator, CategoryTheory.GrpObj.mul_inv, CategoryTheory.IsCommMonObj.mul_comm, CategoryTheory.Functor.obj.μ_def_assoc, mul_one_hom_assoc, CategoryTheory.Mon.mul_def, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_mul, MonObj.unmopMonObj_mul, CategoryTheory.Functor.id_mapMon_mul, mul_braiding, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, CategoryTheory.Functor.mapGrp_obj_grp_mul, CategoryTheory.Functor.mapCommpGrp_id_mul, MonObj.mopEquiv_functor_obj_mon_mul_unmop, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv_assoc, CategoryTheory.Monad.ofMon_μ, CategoryTheory.GrpObj.mul_inv_rev, CategoryTheory.GrpObj.mulRight_hom, CategoryTheory.CommMon.trivial_mon_mul, CategoryTheory.Preadditive.mul_def, CategoryTheory.GrpObj.lift_comp_inv_left_assoc, CategoryTheory.Mod_.regular_mod_smul, CategoryTheory.HopfObj.antipode_comul₁, CategoryTheory.Functor.FullyFaithful.grpObj_mul, CategoryTheory.GrpObj.mulRight_inv, CategoryTheory.Comon.ComonToMonOpOpObj_mon_mul, CategoryTheory.GrpObj.mul_inv_assoc, CategoryTheory.IsCommMonObj.mul_comm_assoc, CategoryTheory.Mon.hom_mul, CategoryTheory.GrpObj.right_inv, CategoryTheory.GrpObj.lift_comp_inv_left, CategoryTheory.GrpObj.eq_lift_inv_left, lift_comp_one_left_assoc, CategoryTheory.HopfObj.mul_antipode₂, mul_assoc_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom_assoc, CategoryTheory.IsCommMonObj.mul_comm', CommGrpTypeEquivalenceCommGrp.inverse_obj_mul, mul_one_assoc, mul_assoc_flip_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, CategoryTheory.CommGrp.trivial_grp_mul, CategoryTheory.Mod_.assoc_flip, CategoryTheory.BimonObj.mul_comul, CategoryTheory.IsMonHom.mul_hom_assoc, Bimod.regular_actLeft, CategoryTheory.GrpObj.ofIso_mul, CategoryTheory.GrpObj.lift_comp_inv_right, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, CategoryTheory.Bimon.mul_counit_assoc, CategoryTheory.ModObj.mul_smul, CategoryTheory.Functor.mapCommGrp_obj_grp_mul, MonObj.mopMonObj_mul_unmop, CategoryTheory.ModObj.mul_smul', CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_mul, one_mul, mul_rightUnitor, CategoryTheory.Bimon.trivial_X_mon_mul, CategoryTheory.HopfObj.antipode_right, mul_one_hom, CategoryTheory.Grp.trivial_grp_mul, CategoryTheory.Bimon.compatibility, one_mul_hom_assoc, CategoryTheory.GrpObj.right_inv_assoc, CategoryTheory.Mon.tensorUnit_mul, instIsMonHomMulOfIsCommMonObj, one_mul_hom, mul_eq_mul, CategoryTheory.Mathlib.Tactic.MonTauto.eq_one_mul, CategoryTheory.GrpObj.lift_inv_comp_right_assoc, CategoryTheory.Comon.monoidal_tensorObj_comon_comul, CategoryTheory.Mon.tensor_mul, mul_assoc_flip, MonObj.mopEquiv_inverse_obj_mon_mul
ofIso 📖CompOp
3 mathmath: ofIso_mul, ofIso_one, CategoryTheory.isMonHom_ofIso
one 📖CompOp
147 mathmath: CategoryTheory.GrpObj.lift_inv_comp_left, CategoryTheory.ModObj.one_smul_assoc, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_one, CategoryTheory.Monad.ofMon_η, CategoryTheory.Functor.mapCommGrp_obj_grp_one, CategoryTheory.BimonObj.one_comul, CategoryTheory.GrpObj.lift_inv_comp_left_assoc, CommGrpTypeEquivalenceCommGrp.inverse_obj_one, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, CategoryTheory.GrpObj.left_inv_assoc, instIsMonHomOne, CategoryTheory.Over.grpObjMkPullbackSnd_one, ofIso_one, lift_comp_one_right, Bimod.actRight_one, ofRepresentableBy_one, CategoryTheory.GrpObj.lift_inv_comp_right, Bimod.TensorBimod.actRight_one', lift_comp_one_right_assoc, CategoryTheory.GrpObj.one_inv_assoc, CategoryTheory.Functor.mapGrp_obj_grp_one, CategoryTheory.Functor.mapGrp_id_one, CategoryTheory.GrpObj.η_whiskerRight_commutator_assoc, CategoryTheory.GrpObj.lift_comp_inv_right_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_one, AlgebraicGeometry.instIsClosedImmersionLeftSchemeDiscretePUnitOneOverSpecOf, MonObj.mopEquiv_functor_obj_mon_one_unmop, MonObj.unmopMonObj_one, CategoryTheory.HopfObj.one_antipode, CategoryTheory.isCommMonObj_iff_commutator_eq_toUnit_η, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul_assoc, CategoryTheory.Mon.tensorObj_one, one_def, one_mul_assoc, CategoryTheory.HopfObj.antipode_left, CategoryTheory.IsMonHom.one_hom_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, CategoryTheory.ModObj.one_smul'_assoc, CategoryTheory.Functor.obj.η_def_assoc, lift_comp_one_left, CategoryTheory.Functor.obj.η_def, CategoryTheory.CommGrp.trivial_grp_one, CategoryTheory.Bimon.one_comul, CategoryTheory.GrpObj.one_inv, CategoryTheory.GrpObj.mulRight_one, CategoryTheory.HopfObj.antipode_comul₂, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul_assoc, tensorObj.one_def, CategoryTheory.HopfObj.antipode_left_assoc, CategoryTheory.Functor.mapMon_obj_mon_one, Bimod.one_actLeft_assoc, mul_one, CategoryTheory.GrpObj.whiskerLeft_η_commutator, CategoryTheory.BimonObj.one_counit_assoc, Mon_tensor_mul_one, CategoryTheory.BimonObj.one_comul_assoc, Mon_tensor_one_mul, CategoryTheory.IsMonHom.one_hom, CategoryTheory.Conv.one_eq, CategoryTheory.Grp.tensorUnit_one, CategoryTheory.Functor.FullyFaithful.monObj_one, CategoryTheory.Mathlib.Tactic.MonTauto.eq_mul_one, CategoryTheory.Over.monObjMkPullbackSnd_one, CategoryTheory.CommGrp.forget₂Grp_obj_one, CategoryTheory.GrpObj.whiskerLeft_η_commutator_assoc, CategoryTheory.ModObj.one_smul', one_leftUnitor, CategoryTheory.Mon.uniqueHomFromTrivial_default_hom, one_braiding, CategoryTheory.Functor.mapCommGrp_id_one, ModuleCat.MonModuleEquivalenceAlgebra.algebraMap, Bimod.one_actLeft, CategoryTheory.HopfObj.mul_antipode₁, CategoryTheory.Mon.trivial_mon_one, CategoryTheory.Functor.mapCommMon_obj_mon_one, CategoryTheory.GrpObj.left_inv, CategoryTheory.Mon.tensorUnit_one, CategoryTheory.HopfObj.antipode_right_assoc, CategoryTheory.CommMon.trivial_mon_one, CommAlgCat.one_op_of_unop_hom, CategoryTheory.BimonObj.one_counit, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_one, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_inverse_obj_laxMonoidal_ε, CategoryTheory.Bimon.ofMonComonObjX_one, CategoryTheory.Grp.tensorObj_one, one_associator, mul_one_hom_assoc, CategoryTheory.Bimon.toMonComonObj_mon_one_hom, CategoryTheory.ModObj.one_smul, CategoryTheory.CommGrp.forget₂CommMon_obj_one, CategoryTheory.Grp.trivial_grp_one, CategoryTheory.Bimon.one_comul_assoc, CategoryTheory.GrpObj.lift_comp_inv_left_assoc, CategoryTheory.Functor.comp_mapCommGrp_one, CategoryTheory.Grp.hom_one, CategoryTheory.Grp.forget₂Mon_obj_one, Bimod.actRight_one_assoc, CategoryTheory.Hom.one_def, CategoryTheory.HopfObj.antipode_comul₁, CategoryTheory.GrpObj.η_whiskerRight_commutator, MonObj.mopMonObj_one_unmop, Bimod.TensorBimod.one_act_left', CategoryTheory.GrpObj.right_inv, CategoryTheory.GrpObj.lift_comp_inv_left, CategoryTheory.Mon.limit_mon_one, lift_comp_one_left_assoc, CategoryTheory.HopfObj.mul_antipode₂, MonObj.mopEquiv_inverse_obj_mon_one, mul_one_assoc, CategoryTheory.Functor.FullyFaithful.grpObj_one, one_rightUnitor, CategoryTheory.Mon.one_def, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_functor_obj_mon_one, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj_ε, CategoryTheory.Preadditive.one_def, AlgebraicGeometry.Scheme.monObjAsOverPullback_one, CategoryTheory.GrpObj.lift_comp_inv_right, one_eq_one, CategoryTheory.Functor.mapCommMon_id_one, CategoryTheory.Monad.one_def, CategoryTheory.GrpObj.ofIso_one, one_mul, CategoryTheory.Functor.id_mapMon_one, CategoryTheory.HopfObj.antipode_right, mul_one_hom, CategoryTheory.Comon.MonOpOpToComonObj_comon_counit, one_mul_hom_assoc, CategoryTheory.GrpObj.right_inv_assoc, CategoryTheory.Mon.tensor_one, CategoryTheory.Mon.hom_one, ModuleCat.MonModuleEquivalenceAlgebra.inverseObj_one, CategoryTheory.HopfObj.one_antipode_assoc, CategoryTheory.Functor.comp_mapMon_one, one_mul_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_one, CategoryTheory.CommMon.forget₂Mon_obj_one, CategoryTheory.Mathlib.Tactic.MonTauto.eq_one_mul, CategoryTheory.GrpObj.lift_inv_comp_right_assoc, CategoryTheory.Functor.comp_mapCommMon_one, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_ε, CategoryTheory.Functor.comp_mapGrp_one, CategoryTheory.Bimon.trivial_X_mon_one, CategoryTheory.Comon.ComonToMonOpOpObj_mon_one
termη 📖CompOp
termμ 📖CompOp
«termη[_]» 📖CompOp
«termμ[_]» 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
Mon_tensor_mul_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategory.comp_whiskerRight_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_comp_assoc
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorμ_natural_left
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
mul_assoc
CategoryTheory.MonoidalCategory.tensor_associativity
CategoryTheory.MonoidalCategory.tensorμ_natural_right
CategoryTheory.MonoidalCategory.tensor_whiskerLeft
CategoryTheory.Iso.inv_hom_id_assoc
Mon_tensor_mul_one 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
one
CategoryTheory.MonoidalCategory.tensorμ
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.whiskerLeft_comp_assoc
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorμ_natural_right
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
mul_one
CategoryTheory.MonoidalCategory.tensor_right_unitality
Mon_tensor_one_mul 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
one
CategoryTheory.MonoidalCategory.tensorμ
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategory.comp_whiskerRight_assoc
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorμ_natural_left
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
one_mul
CategoryTheory.MonoidalCategory.tensor_left_unitality
ext 📖mulCategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.MonoidalCategory.whiskerRight_id
CategoryTheory.Category.assoc
mul_one
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.MonoidalCategory.id_whiskerLeft
one_mul
ext_iff 📖mathematicalmulext
instIsMonHomHomAssociator 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorObj.instTensorObj
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
one_associator
mul_associator
instIsMonHomHomBraiding 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Mon.instMonObjTensorObj
CategoryTheory.SymmetricCategory.toBraidedCategory
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
one_braiding
mul_braiding
instIsMonHomHomLeftUnitor 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
tensorObj.instTensorObj
instTensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
one_leftUnitor
mul_leftUnitor
instIsMonHomHomRightUnitor 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
tensorObj.instTensorObj
instTensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
one_rightUnitor
mul_rightUnitor
instIsMonHomId 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.Category.id_comp
instIsMonHomTensorHom 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorObj.instTensorObj
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.IsMonHom.one_hom
CategoryTheory.MonoidalCategory.tensorμ_natural
CategoryTheory.IsMonHom.mul_hom
instIsMonHomWhiskerLeft 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorObj.instTensorObj
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.IsMonHom.one_hom
instIsMonHomTensorHom
instIsMonHomId
CategoryTheory.IsMonHom.mul_hom
instIsMonHomWhiskerRight 📖mathematicalCategoryTheory.IsMonHom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
tensorObj.instTensorObj
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.IsMonHom.one_hom
instIsMonHomTensorHom
instIsMonHomId
CategoryTheory.IsMonHom.mul_hom
mul_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
mul_assoc_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_assoc
mul_assoc_flip 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
mul
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
mul_assoc
CategoryTheory.Iso.inv_hom_id_assoc
mul_assoc_flip_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
mul
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_assoc_flip
mul_associator 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.MonoidalCategory.associator_naturality
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.associator_monoidal
mul_braiding 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
mul
CategoryTheory.Mon.instMonObjTensorObj
CategoryTheory.SymmetricCategory.toBraidedCategory
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Category.assoc
CategoryTheory.BraidedCategory.braiding_naturality
CategoryTheory.BraidedCategory.braiding_tensor_right_hom
CategoryTheory.BraidedCategory.braiding_tensor_left_hom
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.MonoidalCategory.whisker_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_comp
CategoryTheory.MonoidalCategory.pentagon_assoc
CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv_assoc
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv_assoc
CategoryTheory.SymmetricCategory.symmetry
CategoryTheory.MonoidalCategory.id_whiskerRight
CategoryTheory.MonoidalCategory.whiskerLeft_id
CategoryTheory.Category.id_comp
CategoryTheory.MonoidalCategory.pentagon_inv_assoc
CategoryTheory.Iso.hom_inv_id_assoc
CategoryTheory.MonoidalCategory.associator_inv_naturality_left
CategoryTheory.Iso.inv_hom_id
CategoryTheory.MonoidalCategory.associator_naturality_right
CategoryTheory.MonoidalCategory.tensorHom_def
mul_def 📖mathematicalmul
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategoryStruct.leftUnitor
mul_leftUnitor 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
mul
CategoryTheory.Category.comp_id
CategoryTheory.Category.id_comp
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.leftUnitor_naturality
CategoryTheory.MonoidalCategory.leftUnitor_monoidal
mul_mul_mul_comm 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
mul
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc
CategoryTheory.Category.comp_id
CategoryTheory.Category.assoc
CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv
CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom
CategoryTheory.MonoidalCategory.id_tensorHom_id
CategoryTheory.Category.id_comp
CategoryTheory.IsCommMonObj.mul_comm
CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp_assoc
mul_mul_mul_comm' 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorδ
CategoryTheory.MonoidalCategoryStruct.tensorHom
mul
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc
CategoryTheory.Category.comp_id
CategoryTheory.Category.assoc
CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv
CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom
CategoryTheory.MonoidalCategory.id_tensorHom_id
CategoryTheory.Category.id_comp
CategoryTheory.IsCommMonObj.mul_comm'
CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp_assoc
mul_mul_mul_comm'_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorδ
CategoryTheory.MonoidalCategoryStruct.tensorHom
mul
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_mul_mul_comm'
mul_mul_mul_comm_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
mul
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_mul_mul_comm
mul_one 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
one
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
mul_one_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
one
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_one
mul_one_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
one
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.tensorHom_def_assoc
mul_one
CategoryTheory.MonoidalCategory.rightUnitor_naturality
mul_one_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
one
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_one_hom
mul_rightUnitor 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.Category.id_comp
CategoryTheory.Category.comp_id
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.rightUnitor_naturality
CategoryTheory.MonoidalCategory.rightUnitor_monoidal
ofIso_mul 📖mathematicalmul
ofIso
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.inv
CategoryTheory.Iso.hom
ofIso_one 📖mathematicalone
ofIso
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
one_associator 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
one
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom
CategoryTheory.MonoidalCategory.associator_naturality
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.id_whiskerLeft
CategoryTheory.Iso.hom_inv_id_assoc
one_braiding 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
one
tensorObj.instTensorObj
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.Category.assoc
CategoryTheory.BraidedCategory.braiding_naturality
CategoryTheory.braiding_tensorUnit_right
Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_tensorHom
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.evalHorizontalComp_cons_cons
Mathlib.Tactic.Monoidal.evalHorizontalCompAux_of
Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_cons
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_nil_cons
Mathlib.Tactic.BicategoryLike.mk_eq_of_cons
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_rightUnitor
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_leftUnitor
Mathlib.Tactic.Monoidal.naturality_tensorHom
Mathlib.Tactic.Monoidal.naturality_id
one_def 📖mathematicalone
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorUnit
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
one_leftUnitor 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.CategoryStruct.id
one
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategory.id_tensorHom
CategoryTheory.MonoidalCategory.id_whiskerLeft
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
one_mul 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerRight
one
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
one_mul_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.whiskerRight
one
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
one_mul
one_mul_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
one
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategory.tensorHom_def'_assoc
one_mul
CategoryTheory.MonoidalCategory.leftUnitor_naturality
one_mul_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
one
mul
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
one_mul_hom
one_rightUnitor 📖mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom
one
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategory.tensorHom_id
CategoryTheory.MonoidalCategory.whiskerRight_id
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id

CategoryTheory.MonObj.tensorObj

Definitions

NameCategoryTheorems
instTensorObj 📖CompOp
10 mathmath: CategoryTheory.MonObj.instIsMonHomHomAssociator, CategoryTheory.MonObj.instIsMonHomTensorHom, mul_def, CategoryTheory.MonObj.instIsMonHomHomLeftUnitor, one_def, CategoryTheory.MonObj.instIsMonHomHomRightUnitor, CategoryTheory.MonObj.one_braiding, CategoryTheory.MonObj.instIsMonHomWhiskerLeft, CategoryTheory.MonObj.instIsMonHomWhiskerRight, CategoryTheory.Mon.monMonoidalStruct_tensorHom_hom

Theorems

NameKindAssumesProvesValidatesDepends On
mul_def 📖mathematicalCategoryTheory.MonObj.mul
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategory.tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
one_def 📖mathematicalCategoryTheory.MonObj.one
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorObj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.tensorHom

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