Documentation Verification Report

Cat

📁 Source: Mathlib/CategoryTheory/Monoidal/Cartesian/Cat.lean

Statistics

MetricCount
DefinitionsCat, chosenTerminal, chosenTerminalIsTerminal, fromChosenTerminalEquiv, instBraidedCategory, instCartesianMonoidalCategory, isLimitProdCone, prodCone
8
Theoremsassociator_hom, associator_inv, leftUnitor_hom, leftUnitor_inv, rightUnitor_hom, rightUnitor_inv, tensorHom, tensorObj, tensorUnit, whiskerLeft, whiskerLeft_fst, whiskerLeft_snd, whiskerRight, whiskerRight_fst, whiskerRight_snd
15
Total23

CategoryTheory

Definitions

NameCategoryTheorems
Cat 📖CompOp
597 mathmath: Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, Pseudofunctor.mapComp'_naturality_1_assoc, Join.pseudofunctorLeft_mapId_inv_toNatTrans_app, Pseudofunctor.DescentData.isEquivalence_toDescentData_of_sieve_le, SSet.Truncated.HomotopyCategory.BinaryProduct.iso_inv_toFunctor, Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, Pseudofunctor.DescentData.ofObj_hom, Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_adj, Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, Cat.Hom₂.comp_app, Cat.whiskerRight_toNatTrans, Cat.asSmallFunctor_obj, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_map, Grothendieck.ιCompMap_hom_app_fiber, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, Grpd.forgetToCat_full, ReflQuiv.adj_homEquiv, Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, Cat.freeRefl_map, Pseudofunctor.mapComp_assoc_right_hom_app_assoc, Pseudofunctor.map₂_associator_app_assoc, Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, nerve.instFullCatTruncatedOfNatNatNerveFunctor₂, Pseudofunctor.isEquivalence_toDescentData, Cat.Hom.id_map, Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, Cat.Hom.toNatIso_associator, Cat.associator_hom_app, Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app_assoc, Cat.Hom.inv_hom_id_toNatTrans_assoc, Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, OplaxFunctor.map₂_associator_app, Pseudofunctor.CoGrothendieck.categoryStruct_id_fiber, curryingIso_hom_toFunctor_obj_map, Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, nerve.functorOfNerveMap_map, Pseudofunctor.CoGrothendieck.map_comp_eq, Adjunction.ofCat_counit, Pseudofunctor.mapComp'_comp_id_hom_app, Grothendieck.map_comp_eq, CostructuredArrow.grothendieckPrecompFunctorToComma_map_left, Pseudofunctor.mapComp'_comp_id_inv_app, Grothendieck.pre_comp_map_assoc, Grpd.free_obj, Oplax.StrongTrans.whiskerLeft_naturality_comp_app, Cat.Hom₂.eqToHom_toNatTrans, Cat.Hom₂.id_app, Grothendieck.ιNatTrans_app_fiber, Pseudofunctor.mapComp_assoc_left_inv_app_assoc, nerveFunctor.faithful, Pseudofunctor.DescentData.pullFunctor_map_hom, SSet.hoFunctor.preservesTerminal', Grothendieck.grothendieckTypeToCat_inverse_map_base, CostructuredArrow.functor_obj, Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, Grpd.free_map, instFullCatTypeToCat, Cat.Hom.isoMk_hom, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, Pseudofunctor.mapId'_inv_naturality_assoc, Cat.Hom.toNatIso_hom, Pseudofunctor.mapComp_id_left_inv_app, Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, OplaxFunctor.mapComp_assoc_left_app_assoc, Pseudofunctor.CoGrothendieck.instIsEquivalenceαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, Monoidal.whiskerRight_fst, Functor.equivCatHom_symm_apply, Grothendieck.compAsSmallFunctorEquivalenceFunctor_map_fiber, Pseudofunctor.DescentData.isoMk_inv_hom, Cat.Hom₂.comp_app_assoc, Grothendieck.grothendieckTypeToCatFunctor_obj_snd, Pseudofunctor.CoGrothendieck.map_map_base, Pseudofunctor.CoGrothendieck.map_map_fiber, Pseudofunctor.Grothendieck.map_id_eq, Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_l, Pseudofunctor.ObjectProperty.ι_app_toFunctor, LaxFunctor.mapComp_naturality_left_app_assoc, Pseudofunctor.DescentData.comp_hom, Cat.leftUnitor_hom_app, Grothendieck.isoMk_inv_fiber, OplaxFunctor.map₂_leftUnitor_app, Cat.Hom.inv_hom_id_toNatTrans, ReflQuiv.adj_unit_app, flippingIso_inv_toFunctor_obj_obj_obj, Adjunction.toCat_comp_toCat, Pseudofunctor.Grothendieck.ext_iff, Cat.Hom.isoMk_inv, CostructuredArrow.grothendieckPrecompFunctorEquivalence_functor, Pseudofunctor.mapComp'_inv_naturality, Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app, CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, Pseudofunctor.ObjectProperty.fullsubcategory_mapComp, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_obj, CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_fiber, Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, Under.mapFunctor_obj, Cat.exp_obj, LaxFunctor.mapComp_assoc_right_app, Cat.opEquivalence_counitIso, Pseudofunctor.mapComp'_naturality_1, MonCat.toCat_faithful, Pseudofunctor.isStackFor_ofArrows_iff, LaxFunctor.map₂_leftUnitor_hom_app, CostructuredArrow.ιCompGrothendieckProj_inv_app, Pseudofunctor.mapComp'₀₁₃_hom_app, Grothendieck.id_fiber, Cat.ihom_obj, Join.pseudofunctorLeft_mapId_hom_toNatTrans_app, Pseudofunctor.mapComp_id_right_inv_app_assoc, Functor.hasColimit_map_comp_ι_comp_grothendieckProj, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_val_app, Pseudofunctor.map₂_associator_app, Cat.rightUnitor_hom_toNatTrans, GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, flippingIso_inv_toFunctor_obj_map_app, StructuredArrow.functor_map, Pseudofunctor.DescentData.iso_hom, Functor.equivCatHom_apply, Pseudofunctor.mapComp'_comp_id_inv_app_assoc, Cat.instHasTerminal, Pseudofunctor.mapComp'_inv_naturality_assoc, Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, Pseudofunctor.presheafHom_obj, Pseudofunctor.mapComp_assoc_right_inv_app, Cat.HasLimits.limitCone_π_app, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapId, Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CostructuredArrow.grothendieckPrecompFunctorToComma_obj_right, Cat.free_map, CostructuredArrow.commaToGrothendieckPrecompFunctor_map_base, Pseudofunctor.DescentData.iso_inv, Cat.HasLimits.limitCone_pt, OplaxFunctor.mapComp_assoc_left_app, Cat.HasLimits.homDiagram_map, Pseudofunctor.CoGrothendieck.instFullαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, Oplax.StrongTrans.whiskerRight_naturality_naturality_app, Pseudofunctor.DescentData.nonempty_fullyFaithful_toDescentData_iff_of_sieve_eq, Cat.associator_inv_app, Cat.Hom.comp_toFunctor, Grothendieck.ιNatTrans_app_base, Cat.rightUnitor_hom_app, Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, Pseudofunctor.ObjectProperty.ι_naturality, Cat.opFunctor_obj, LaxFunctor.mapComp_naturality_right_app_assoc, Grothendieck.comp_fiber, Grothendieck.map_map, Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, Grothendieck.ιCompMap_inv_app_fiber, instFaithfulPreordCatPreordToCat, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_obj, Pseudofunctor.Grothendieck.map_id_map, Pseudofunctor.ObjectProperty.mapId_inv_app, Nerve.instIsStrictSegalObjCatTruncatedOfNatNatNerveFunctor₂, Monoidal.whiskerRight, OplaxFunctor.map₂_associator_app_assoc, Pseudofunctor.mapComp_id_left_hom_app_assoc, LaxFunctor.map₂_associator_app_assoc, Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans, SSet.hoFunctor.unitHomEquiv_eq, Cat.HasLimits.limitConeX_α, ReflQuiv.forget_map, Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app, Pseudofunctor.DescentData.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpHom, Pseudofunctor.whiskerLeft_mapId_inv_app, LaxFunctor.map₂_leftUnitor_hom_app_assoc, Grothendieck.grothendieckTypeToCat_functor_obj_fst, Monoidal.tensorHom, Pseudofunctor.mapComp'₀₂₃_hom_app, Adjunction.toCat_counit_toNatTrans, OplaxFunctor.mapComp_assoc_right_app, Pseudofunctor.CoGrothendieck.ι_map_base, ReflQuiv.adj.unit.map_app_eq, Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, CommRingCat.moduleCatRestrictScalarsPseudofunctor_map, Pseudofunctor.isPrestackFor_ofArrows_iff, hoFunctor.preservesFiniteProducts, Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, Bicategory.Adjunction.ofCat_id, Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_obj, CatEnrichedOrdinary.Hom.mk_comp, Pseudofunctor.CoGrothendieck.map_obj_fiber, Bicategory.Adjunction.ofCat_comp, Pseudofunctor.ObjectProperty.mapComp_hom_app, NatTrans.toCatHom₂_id, Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, curryingIso_inv_toFunctor_obj_map_app, LaxFunctor.map₂_rightUnitor_hom_app, Pseudofunctor.DescentData.Hom.comm_assoc, Grothendieck.fiber_eqToHom, WithInitial.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_obj, SSet.Truncated.HomotopyCategory.BinaryProduct.left_unitality, Monoidal.rightUnitor_hom, Grothendieck.eqToHom_eq, curryingIso_hom_toFunctor_obj_obj, Cat.opEquivalence_unitIso, Pseudofunctor.mapComp_id_left_inv_app_assoc, WithInitial.prelaxfunctor_toPrelaxFunctorStruct_map₂, hoFunctor.instIsLeftAdjointSSetCatHoFunctor, Oplax.StrongTrans.whiskerLeft_naturality_id_app, Pseudofunctor.mapComp'_hom_naturality_assoc, Pseudofunctor.mapComp'_naturality_2_assoc, Pseudofunctor.Grothendieck.categoryStruct_id_fiber, Quiv.forget_map, Pseudofunctor.ObjectProperty.map_map_hom, CostructuredArrow.grothendieckPrecompFunctorToComma_obj_left, SimplexCategory.toCat.obj_eq_Fin, Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, Grothendieck.compAsSmallFunctorEquivalenceFunctor_obj_fiber, Cat.Hom.hom_inv_id_toNatTrans, Cat.exp_map, Pseudofunctor.CoGrothendieck.Hom.congr, Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, CatEnrichedOrdinary.Hom.id_eq, ReflQuiv.forget_obj, Grothendieck.grothendieckTypeToCat_inverse_obj_base, Pseudofunctor.mapComp'_id_comp_inv_app_assoc, Grpd.freeForgetAdjunction_homEquiv_symm_apply, Cat.isoOfEquiv_inv, Grothendieck.grothendieckTypeToCatFunctor_map_coe, Quiv.adj_homEquiv, Cat.isoOfEquiv_hom, Grothendieck.compAsSmallFunctorEquivalenceInverse_obj_fiber, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, SSet.hoFunctor.preservesTerminal, Cat.HasLimits.limit_π_homDiagram_eqToHom, Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, OplaxFunctor.mapComp_naturality_left_app, Grothendieck.pre_map_fiber, CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, Cat.opFunctor_map, flippingIso_inv_toFunctor_map_app_app, Cat.Hom.comp_map, Grothendieck.map_id_eq, Cat.opFunctorInvolutive_hom_app_toFunctor_map, Pseudofunctor.DescentData.ofObj_obj, Cat.opFunctorInvolutive_hom_app_toFunctor_obj, LaxFunctor.map₂_rightUnitor_hom_app_assoc, Pseudofunctor.StrongTrans.naturality_id_hom_app, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_val_app, Pseudofunctor.CoGrothendieck.ext_iff, Cat.HasLimits.limitConeX_str, Cat.instHasLimits, CostructuredArrow.functor_map, Pseudofunctor.DescentData.hom_comp_assoc, Pseudofunctor.Grothendieck.map_obj_fiber, Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, Monoidal.associator_hom, Pseudofunctor.mapComp_assoc_left_hom_app_assoc, Grothendieck.compAsSmallFunctorEquivalence_functor, Cat.opEquivalence_inverse, Pseudofunctor.CoGrothendieck.ι_obj_fiber, SSet.Truncated.HomotopyCategory.BinaryProduct.iso_hom_toFunctor, Pseudofunctor.isStackFor_iff, CommRingCat.moduleCatExtendScalarsPseudofunctor_map, Under.mapFunctor_map, CostructuredArrow.grothendieckPrecompFunctorEquivalence_unitIso, Pseudofunctor.bijective_toDescentData_map_iff, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, Join.pseudofunctorRight_mapId_hom_toNatTrans_app, Grpd.forgetToCat_faithful, Pseudofunctor.CoGrothendieck.ι_map_fiber, ReflQuiv.forget_forgetToQuiv, nerveFunctor_map, Grothendieck.toTransport_fiber, Codiscrete.adj_counit_app, OplaxFunctor.mapComp_assoc_right_app_assoc, Cat.HasLimits.id_def, Monoidal.whiskerLeft_snd, CatEnrichedOrdinary.Hom.base_comp, RingCat.moduleCatRestrictScalarsPseudofunctor_mapId, Cat.free_obj, Grothendieck.pre_obj_base, Pseudofunctor.DescentData.pullFunctorObj_obj, Cat.opEquivalence_functor, Cat.opFunctorInvolutive_inv_app_toFunctor_map, flippingIso_hom_toFunctor_obj_obj_map, Functor.elementsFunctor_map, CostructuredArrow.grothendieckProj_map, SSet.Truncated.hoFunctor₂_naturality, CommRingCat.moduleCatExtendScalarsPseudofunctor_obj, Grothendieck.grothendieckTypeToCatFunctor_obj_fst, Grpd.freeForgetAdjunction_counit_app, ReflQuiv.adj_counit_app, hoFunctor.preservesBinaryProducts, Grothendieck.compAsSmallFunctorEquivalence_inverse, Pseudofunctor.StrongTrans.naturality_comp_inv_app, WithInitial.pseudofunctor_mapId, Grothendieck.pre_comp_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, Join.pseudofunctorRight_mapId_inv_toNatTrans_app, RingCat.moduleCatRestrictScalarsPseudofunctor_map, instFullPreordCatPreordToCat, Pseudofunctor.ObjectProperty.IsClosedUnderMapObj.map_obj, Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app_assoc, Pseudofunctor.mapComp'_hom_naturality, CostructuredArrow.grothendieckPrecompFunctorEquivalence_inverse, Grothendieck.map_obj_fiber, ReflQuiv.forget.Faithful, Cat.comp_eq_comp, Grothendieck.compAsSmallFunctorEquivalenceFunctor_obj_base, Cat.leftUnitor_hom_toNatTrans, Cat.ihom_map, Pseudofunctor.mapComp'_comp_id_hom_app_assoc, hoFunctor.isIso_prodComparison_stdSimplex, AlgebraicGeometry.Scheme.Modules.pseudofunctor_obj_obj, WithInitial.pseudofunctor_toPrelaxFunctor, Pseudofunctor.IsStack.essSurj_of_sieve, Bicategory.toNatTrans_mateEquiv, CostructuredArrow.preFunctor_app, Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, Cat.Hom.hom_inv_id_toNatTrans_assoc, Pseudofunctor.mapComp_assoc_right_hom_app, Cat.associator_inv_toNatTrans, WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_map₂, Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, Monoidal.tensorUnit, Cat.leftUnitor_inv_toNatTrans, Pseudofunctor.map₂_left_unitor_app, Cat.Hom.inv_hom_id_toNatTrans_app_assoc, Grothendieck.compAsSmallFunctorEquivalenceFunctor_map_base, CatEnrichedOrdinary.Hom.comp_eq, Pseudofunctor.ObjectProperty.mapId_hom_app, Grothendieck.ιCompMap_inv_app_base, Pseudofunctor.whiskerLeft_mapId_hom_app, nerve_map, CatEnriched.comp_eq, Cat.Hom.instIsIsoFunctorαCategoryToNatTransInvHom, Pseudofunctor.toDescentData_obj, Cat.Hom.toNatIso_leftUnitor, Pseudofunctor.map₂_whisker_right_app_assoc, Grothendieck.pre_comp, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, Pseudofunctor.presheafHomObjHomEquiv_apply, Cat.Hom.toNatIso_rightUnitor, Cat.Hom.id_obj, MonCat.toCat_full, curryingIso_inv_toFunctor_obj_obj_obj, Pseudofunctor.mapComp_assoc_right_inv_app_assoc, WithTerminal.pseudofunctor_toPrelaxFunctor, nerveFunctor.full, LaxFunctor.mapComp_assoc_left_app, Grothendieck.transportIso_inv_fiber, Cat.rightUnitor_inv_app, Pseudofunctor.mapComp'_id_comp_hom_app_assoc, Pseudofunctor.Grothendieck.Hom.ext_iff, Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, CatEnrichedOrdinary.homEquiv_comp, Grothendieck.map_obj, Cat.Hom.toNatTrans_id, Cat.opFunctorInvolutive_inv_app_toFunctor_obj, Cat.rightUnitor_inv_toNatTrans, Pseudofunctor.isPrestackFor_iff, Pseudofunctor.IsStackFor.isEquivalence, Pseudofunctor.StrongTrans.naturality_id_inv_app, Adjunction.toCat_unit_toNatTrans, Pseudofunctor.CoGrothendieck.instEssSurjαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, Pseudofunctor.whiskerRight_mapId_hom_app_assoc, Cat.Hom.comp_obj, RingCat.moduleCatRestrictScalarsPseudofunctor_obj, Oplax.StrongTrans.whiskerRight_naturality_comp_app, Pseudofunctor.Grothendieck.Hom.congr, Grpd.freeForgetAdjunction_homEquiv_apply, Pseudofunctor.Grothendieck.map_comp_eq, NatTrans.toCatHom₂_comp, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_map, Pseudofunctor.Grothendieck.map_map_fiber, Pseudofunctor.map₂_whisker_left_app_assoc, Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, Grothendieck.compAsSmallFunctorEquivalenceInverse_obj_base, Pseudofunctor.mapComp'_naturality_2, Pseudofunctor.CoGrothendieck.ι_obj_base, flippingIso_hom_toFunctor_obj_map_app, Pseudofunctor.mapComp_id_right_inv_app, Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app_assoc, Pseudofunctor.mapComp_id_left_hom_app, CostructuredArrow.grothendieckPrecompFunctorEquivalence_counitIso, CostructuredArrow.grothendieckProj_obj, Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, Pseudofunctor.toDescentData_map_hom, Pseudofunctor.ObjectProperty.IsClosedUnderIsomorphisms.isClosedUnderIsomorphisms, RingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, Cat.freeRefl_obj, Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, Pseudofunctor.DescentData.pullFunctorObjHom_eq_assoc, LaxFunctor.map₂_rightUnitor_app_assoc, preordToCat_obj, Functor.elementsFunctor_obj, Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, preordToCat_map, Codiscrete.adj_unit_app, curryingIso_inv_toFunctor_map_app_app, ReflQuiv.adj.counit.comp_app_eq, Grothendieck.final_pre, WithTerminal.pseudofunctor_mapId, Grothendieck.compAsSmallFunctorEquivalenceInverse_map_fiber, StructuredArrow.functor_obj, Pseudofunctor.IsStackFor.essSurj, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_map, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, WithInitial.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_map, LaxFunctor.map₂_rightUnitor_app, Grothendieck.compAsSmallFunctorEquivalence_unitIso, Grothendieck.grothendieckTypeToCat_inverse_obj_fiber_as, Pseudofunctor.mapComp'_id_comp_inv_app, Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, CatEnriched.id_eq, SimplexCategory.toCat_obj, Cat.HasLimits.comp_def, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapComp, WithTerminal.pseudofunctor_mapComp, Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_obj, Over.mapFunctor_obj, Cat.Hom.hom_inv_id_toNatTrans_app, Monoidal.whiskerRight_snd, CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq, instFaithfulCatTypeToCat, Oplax.StrongTrans.whiskerRight_naturality_id_app, flippingIso_inv_toFunctor_obj_obj_map, Pseudofunctor.mapComp_id_right_hom_app_assoc, hoFunctor.instIsIsoCatProdComparisonSSetHoFunctorNerve, Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.right_unitality, Pseudofunctor.map₂_whisker_left_app, Pseudofunctor.DescentData.isEquivalence_toDescentData_iff_of_sieve_eq, Pseudofunctor.CoGrothendieck.comp_const, WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_map, hoFunctor.preservesBinaryProduct, nerve.functorOfNerveMap_nerveFunctor₂_map, Grothendieck.transport_fiber, Pseudofunctor.whiskerRight_mapId_inv_app, Pseudofunctor.CoGrothendieck.map_id_eq, Pseudofunctor.CoGrothendieck.compIso_inv_app, OplaxFunctor.map₂_leftUnitor_app_assoc, Cat.HasLimits.limitConeLift_toFunctor, nerveFunctor_obj, Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, Pseudofunctor.mapComp'_id_comp_hom_app, Grothendieck.map_map_fiber, GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, typeToCat_obj, Cat.asSmallFunctor_map, Monoidal.associator_inv, Grothendieck.map_map_base, Monoidal.rightUnitor_inv, Monoidal.whiskerLeft, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, Grothendieck.ι_obj, Adjunction.ofCat_unit, OplaxFunctor.map₂_rightUnitor_app, Pseudofunctor.mapComp_assoc_left_hom_app, Cat.Hom.toNatTrans_comp, LaxFunctor.mapComp_naturality_right_app, Cat.id_eq_id, Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom, Pseudofunctor.mapComp_id_right_hom_app, flippingIso_hom_toFunctor_obj_obj_obj, Pseudofunctor.DescentData.id_hom, Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, LaxFunctor.mapComp_naturality_left_app, Cat.bicategory.strict, typeToCat_map, Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, Pseudofunctor.StrongTrans.naturality_naturality_hom_app, Pseudofunctor.DescentData.isoMk_hom_hom, flippingIso_hom_toFunctor_map_app_app, Pseudofunctor.DescentData.pullFunctorObjHom_eq, CostructuredArrow.grothendieckPrecompFunctorToComma_map_right, Grothendieck.ιCompMap_hom_app_base, Pseudofunctor.mapId'_hom_naturality, Pseudofunctor.DescentData.hom_self, Grothendieck.compAsSmallFunctorEquivalenceInverse_map_base, Pseudofunctor.DescentData.comp_hom_assoc, Pseudofunctor.mapComp'₀₂₃_inv_app, Cat.Hom.inv_hom_id_toNatTrans_app, Pseudofunctor.ObjectProperty.fullsubcategory_mapId, Pseudofunctor.ObjectProperty.map_obj_obj, Monoidal.tensorObj, Cat.Hom.hom_inv_id_toNatTrans_app_assoc, Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, Cat.whiskerLeft_toNatTrans, Pseudofunctor.mapId'_hom_naturality_assoc, OplaxFunctor.mapComp_naturality_right_app_assoc, Bicategory.toNatTrans_conjugateEquiv, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapId, Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, Cat.instPreservesLimitsObjects, Grothendieck.pre_obj_fiber, Grothendieck.grothendieckTypeToCatInverse_obj_base, Pseudofunctor.map₂_whisker_right_app, curryingIso_inv_toFunctor_obj_obj_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_r, Pseudofunctor.CoGrothendieck.instFaithfulαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, nerve.functorOfNerveMap_obj, CostructuredArrow.ιCompGrothendieckProj_hom_app, WithInitial.pseudofunctor_mapComp, Monoidal.whiskerLeft_fst, nerve.nerveFunctor₂_map_functorOfNerveMap, Grpd.freeForgetAdjunction_unit_app, Pseudofunctor.map₂_left_unitor_app_assoc, Pseudofunctor.map₂_right_unitor_app_assoc, Pseudofunctor.map₂_right_unitor_app, Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, Cat.Hom.equivFunctor_apply, Pseudofunctor.CoGrothendieck.map_id_map, Cat.Hom.toNatIso_inv, Grothendieck.pre_id, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, SimplexCategory.toCat_map, Cat.HasLimits.homDiagram_obj, Grothendieck.grothendieckTypeToCatInverse_map_base, OplaxFunctor.mapComp_naturality_left_app_assoc, Pseudofunctor.presheafHomObjHomEquiv_symm_apply, Cat.whiskerRight_app, LaxFunctor.map₂_associator_app, Grothendieck.congr, Over.mapFunctor_map, Grothendieck.grothendieckTypeToCat_functor_map_coe, CommRingCat.moduleCatRestrictScalarsPseudofunctor_obj, Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, Cat.associator_hom_toNatTrans, Cat.Hom.instIsIsoFunctorαCategoryToNatTransHomHom, Cat.Hom.id_toFunctor, Grothendieck.isoMk_hom_fiber, Monoidal.leftUnitor_inv, Grothendieck.grothendieckTypeToCat_functor_obj_snd, Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, hoFunctor.isIso_prodComparison, GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, Pseudofunctor.ObjectProperty.mapComp_inv_app, CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_base, Grothendieck.compAsSmallFunctorEquivalence_counitIso, curryingIso_hom_toFunctor_map_app, LaxFunctor.mapComp_assoc_right_app_assoc, instIsIsoSSetProdComparisonCatCompNerveFunctorHoFunctorOf, Grothendieck.grothendieckTypeToCatInverse_obj_fiber_as, nerveAdjunction.isIso_counit, CatEnrichedOrdinary.homEquiv_id, OplaxFunctor.mapComp_naturality_right_app, Cat.instHasColimits, LaxFunctor.mapComp_assoc_left_app_assoc, Cat.leftUnitor_inv_app, Monoidal.leftUnitor_hom, LaxFunctor.map₂_leftUnitor_app, Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, CatEnrichedOrdinary.Hom.base_eqToHom, Pseudofunctor.Grothendieck.categoryStruct_comp_fiber, CostructuredArrow.grothendieckPrecompFunctorToComma_obj_hom, nerve.instFaithfulCatTruncatedOfNatNatNerveFunctor₂, Pseudofunctor.whiskerRight_mapId_hom_app, Quiv.forget_obj, Grothendieck.transportIso_hom_fiber, Pseudofunctor.CoGrothendieck.compIso_hom_app, Pseudofunctor.DescentData.hom_comp, Pseudofunctor.IsPrestackFor.nonempty_fullyFaithful, Cat.Hom.equivFunctor_symm_apply, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, Grothendieck.pre_map_base, Cat.whiskerLeft_app, Pseudofunctor.ObjectProperty.map₂_app_hom, Pseudofunctor.CoGrothendieck.Hom.ext_iff, OplaxFunctor.map₂_rightUnitor_app_assoc, Pseudofunctor.Grothendieck.map_map_base, LaxFunctor.map₂_leftUnitor_app_assoc, Cat.eqToHom_app, Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor, Grothendieck.ι_map, Pseudofunctor.whiskerRight_mapId_inv_app_assoc, Pseudofunctor.StrongTrans.naturality_comp_hom_app, Grothendieck.faithful_ι, CatEnrichedOrdinary.Hom.base_id, Pseudofunctor.mapId'_inv_naturality, Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, Pseudofunctor.mapComp'₀₁₃_inv_app, Pseudofunctor.mapComp_assoc_left_inv_app, Pseudofunctor.DescentData.Hom.comm, Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map

CategoryTheory.Cat

Definitions

NameCategoryTheorems
chosenTerminal 📖CompOp
4 mathmath: SSet.hoFunctor.unitHomEquiv_eq, SSet.Truncated.HomotopyCategory.BinaryProduct.left_unitality, CategoryTheory.Monoidal.tensorUnit, SSet.Truncated.HomotopyCategory.BinaryProduct.right_unitality
chosenTerminalIsTerminal 📖CompOp—
fromChosenTerminalEquiv 📖CompOp—
instBraidedCategory 📖CompOp—
instCartesianMonoidalCategory 📖CompOp
32 mathmath: CategoryTheory.Monoidal.whiskerRight_fst, ihom_obj, CategoryTheory.Monoidal.whiskerRight, SSet.hoFunctor.unitHomEquiv_eq, CategoryTheory.Monoidal.tensorHom, CategoryTheory.CatEnrichedOrdinary.Hom.mk_comp, CategoryTheory.Monoidal.rightUnitor_hom, CategoryTheory.CatEnrichedOrdinary.Hom.id_eq, CategoryTheory.Monoidal.associator_hom, CategoryTheory.Monoidal.whiskerLeft_snd, CategoryTheory.CatEnrichedOrdinary.Hom.base_comp, ihom_map, CategoryTheory.hoFunctor.isIso_prodComparison_stdSimplex, CategoryTheory.Monoidal.tensorUnit, CategoryTheory.CatEnrichedOrdinary.Hom.comp_eq, CategoryTheory.CatEnriched.comp_eq, CategoryTheory.CatEnrichedOrdinary.homEquiv_comp, CategoryTheory.CatEnriched.id_eq, CategoryTheory.Monoidal.whiskerRight_snd, CategoryTheory.hoFunctor.instIsIsoCatProdComparisonSSetHoFunctorNerve, CategoryTheory.Monoidal.associator_inv, CategoryTheory.Monoidal.rightUnitor_inv, CategoryTheory.Monoidal.whiskerLeft, CategoryTheory.Monoidal.tensorObj, CategoryTheory.Monoidal.whiskerLeft_fst, CategoryTheory.Monoidal.leftUnitor_inv, CategoryTheory.hoFunctor.isIso_prodComparison, CategoryTheory.instIsIsoSSetProdComparisonCatCompNerveFunctorHoFunctorOf, CategoryTheory.CatEnrichedOrdinary.homEquiv_id, CategoryTheory.Monoidal.leftUnitor_hom, CategoryTheory.CatEnrichedOrdinary.Hom.base_eqToHom, CategoryTheory.CatEnrichedOrdinary.Hom.base_id
isLimitProdCone 📖CompOp—
prodCone 📖CompOp—

CategoryTheory.Monoidal

Theorems

NameKindAssumesProvesValidatesDepends On
associator_hom 📖mathematical—CategoryTheory.Iso.hom
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Functor.toCatHom
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.prod'
CategoryTheory.uniformProd
CategoryTheory.Cat.str
CategoryTheory.Functor.prod'
CategoryTheory.Functor.comp
CategoryTheory.Prod.fst
CategoryTheory.Prod.snd
——
associator_inv 📖mathematical—CategoryTheory.Iso.inv
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Functor.toCatHom
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.prod'
CategoryTheory.Cat.str
CategoryTheory.uniformProd
CategoryTheory.Functor.prod'
CategoryTheory.Prod.fst
CategoryTheory.Functor.comp
CategoryTheory.Prod.snd
——
leftUnitor_hom 📖mathematical—CategoryTheory.Iso.hom
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.Functor.toCatHom
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.prod'
CategoryTheory.Cat.str
CategoryTheory.Prod.snd
——
leftUnitor_inv 📖mathematical—CategoryTheory.Iso.inv
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.Functor.toCatHom
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.Bundled.str
CategoryTheory.prod'
CategoryTheory.Cat.str
CategoryTheory.Prod.sectR
CategoryTheory.ULiftHom
CategoryTheory.Discrete
——
rightUnitor_hom 📖mathematical—CategoryTheory.Iso.hom
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.Functor.toCatHom
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.prod'
CategoryTheory.Cat.str
CategoryTheory.Prod.fst
——
rightUnitor_inv 📖mathematical—CategoryTheory.Iso.inv
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.Functor.toCatHom
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.Bundled.str
CategoryTheory.prod'
CategoryTheory.Cat.str
CategoryTheory.Prod.sectL
CategoryTheory.ULiftHom
CategoryTheory.Discrete
——
tensorHom 📖mathematical—CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.Functor.toCatHom
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.prod'
CategoryTheory.Cat.str
CategoryTheory.Functor.prod
CategoryTheory.Cat.Hom.toFunctor
——
tensorObj 📖mathematical—CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.Cat.of
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.uniformProd
CategoryTheory.Cat.str
——
tensorUnit 📖mathematical—CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.Cat.chosenTerminal
——
whiskerLeft 📖mathematical—CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.Functor.toCatHom
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.prod'
CategoryTheory.Cat.str
CategoryTheory.Functor.prod
CategoryTheory.Functor.id
CategoryTheory.Cat.Hom.toFunctor
——
whiskerLeft_fst 📖mathematical—CategoryTheory.Functor.comp
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.Cat.str
CategoryTheory.Cat.Hom.toFunctor
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Prod.fst
——
whiskerLeft_snd 📖mathematical—CategoryTheory.Functor.comp
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.Cat.str
CategoryTheory.Cat.Hom.toFunctor
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Prod.snd
CategoryTheory.prod'
——
whiskerRight 📖mathematical—CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.Functor.toCatHom
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.prod'
CategoryTheory.Cat.str
CategoryTheory.Functor.prod
CategoryTheory.Cat.Hom.toFunctor
CategoryTheory.Functor.id
——
whiskerRight_fst 📖mathematical—CategoryTheory.Functor.comp
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.Cat.str
CategoryTheory.Cat.Hom.toFunctor
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Prod.fst
CategoryTheory.prod'
——
whiskerRight_snd 📖mathematical—CategoryTheory.Functor.comp
CategoryTheory.Bundled.α
CategoryTheory.Category
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Cat
CategoryTheory.Cat.category
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Cat.instCartesianMonoidalCategory
CategoryTheory.Cat.str
CategoryTheory.Cat.Hom.toFunctor
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Prod.snd
——

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