Cat

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

Statistics

Metric	Count
Definitions Cat, chosenTerminal, chosenTerminalIsTerminal, fromChosenTerminalEquiv, instBraidedCategory, instCartesianMonoidalCategory, isLimitProdCone, prodCone	8
Theorems associator_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
Total	23

CategoryTheory

Definitions

Name	Category	Theorems
Cat 📖	CompOp	729 math math: 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, Pseudofunctor.DescentData'.comm, Cat.Hom₂.comp_app, Cat.whiskerRight_toNatTrans, Cat.asSmallFunctor_obj, Pseudofunctor.isEquivalence_toDescentDataAsCoalgebra_iff_isEquivalence_comonadComparison, 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, Pseudofunctor.DescentData'.comp_pullHom', Limits.fiberwiseColimit_map, Cat.Hom.id_map, Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, Cat.Hom.toNatIso_associator, Pseudofunctor.DescentData'.pullHom'_eq_pullHom_assoc, Pseudofunctor.DescentData'.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpPullbackHom, Cat.associator_hom_app, Pseudofunctor.DescentDataAsCoalgebra.counit, Bicategory.associatorNatIsoLeftCat_hom_toNatTrans_app, Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_inverse_obj_hom, 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, Bicategory.postcomp₂_app_toFunctor_obj, 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, Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str, Pseudofunctor.mapId'_inv_naturality_assoc, Cat.Hom.toNatIso_hom, Pseudofunctor.mapComp_id_left_inv_app, Limits.fiberwiseColimit_obj, Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, OplaxFunctor.mapComp_assoc_left_app_assoc, Pseudofunctor.CoGrothendieck.instIsEquivalenceαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, Monoidal.whiskerRight_fst, Functor.equivCatHom_symm_apply, GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_hom_app, 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.DescentData'.pullHom'_self', Pseudofunctor.Grothendieck.map_id_eq, Pseudofunctor.toDescentDataAsCoalgebraCompCoalgebraEquivalenceFunctorIso_inv_app_f, 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, Bicategory.Adj.counit_naturality, OplaxFunctor.map₂_leftUnitor_app, Cat.Hom.inv_hom_id_toNatTrans, ReflQuiv.adj_unit_app, flippingIso_inv_toFunctor_obj_obj_obj, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_naturality_inv_toNatTrans_app, Adjunction.toCat_comp_toCat, Pseudofunctor.Grothendieck.ext_iff, Cat.Hom.isoMk_inv, CostructuredArrow.grothendieckPrecompFunctorEquivalence_functor, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, 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, Limits.fiberwiseColimitLimitIso_hom_app, Pseudofunctor.mapComp'_naturality_1, MonCat.toCat_faithful, Pseudofunctor.toDescentDataAsCoalgebra_obj_obj, Pseudofunctor.isStackFor_ofArrows_iff, LaxFunctor.map₂_leftUnitor_hom_app, CostructuredArrow.ιCompGrothendieckProj_inv_app, Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_unitIso_inv_app_hom, 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, Pseudofunctor.map₂_associator_app, Cat.rightUnitor_hom_toNatTrans, Bicategory.precomposingCat_map, 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, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_mapComp_inv_toNatTrans_app, Pseudofunctor.mapComp'_inv_naturality_assoc, Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_obj_obj, Pseudofunctor.DescentDataAsCoalgebra.coassoc_assoc, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_mapId_hom_toNatTrans_app, Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, Pseudofunctor.presheafHom_obj, Pseudofunctor.mapComp_assoc_right_inv_app, Pseudofunctor.DescentData'.comp_hom, 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'.isoMk_inv_hom, Pseudofunctor.DescentData.iso_inv, Cat.HasLimits.limitCone_pt, OplaxFunctor.mapComp_assoc_left_app, Bicategory.Adj.left_triangle_components_assoc, Cat.HasLimits.homDiagram_map, Bicategory.associatorNatIsoRightCat_inv_toNatTrans_app, Bicategory.Adj.unit_naturality, Pseudofunctor.CoGrothendieck.instFullαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, Oplax.StrongTrans.whiskerRight_naturality_naturality_app, Pseudofunctor.DescentData.nonempty_fullyFaithful_toDescentData_iff_of_sieve_eq, Cat.associator_inv_app, Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, Cat.Hom.comp_toFunctor, Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, Grothendieck.ιNatTrans_app_base, Cat.rightUnitor_hom_app, Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_hom_app, 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, 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, Pseudofunctor.toDescentDataAsCoalgebra_map_hom, Grothendieck.grothendieckTypeToCat_functor_obj_fst, Bicategory.postcomposing₂_map_as_app_toNatTrans_app, Monoidal.tensorHom, Pseudofunctor.mapComp'₀₂₃_hom_app, Adjunction.toCat_counit_toNatTrans, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, 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.DescentData'.comp_pullHom'', Bicategory.postcomposing₂_obj_naturality_hom_toNatTrans_app, Pseudofunctor.isPrestackFor_ofArrows_iff, hoFunctor.preservesFiniteProducts, Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, Bicategory.Adjunction.ofCat_id, Bicategory.Adj.right_triangle_components, Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_obj, Pseudofunctor.DescentDataAsCoalgebra.Hom.comm, CatEnrichedOrdinary.Hom.mk_comp, Pseudofunctor.CoGrothendieck.map_obj_fiber, Bicategory.Adjunction.ofCat_comp, Pseudofunctor.ObjectProperty.mapComp_hom_app, Limits.ι_colimitFiberwiseColimitIso_hom_assoc, 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, hoFunctor.isIso_prodComparison_of_stdSimplex, 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, Limits.ι_colimitFiberwiseColimitIso_inv_assoc, hoFunctor.instIsLeftAdjointSSetCatHoFunctor, Oplax.StrongTrans.whiskerLeft_naturality_id_app, Pseudofunctor.mapComp'_hom_naturality_assoc, Pseudofunctor.mapComp'_naturality_2_assoc, Limits.hasColimit_ι_comp, 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, Bicategory.postcomposingCat_obj, 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, Bicategory.Adj.unit_naturality_assoc, Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, OplaxFunctor.mapComp_naturality_left_app, Grothendieck.pre_map_fiber, Pseudofunctor.DescentData'.comp_hom_assoc, CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, Cat.opFunctor_map, Pseudofunctor.toDescentDataAsCoalgebra_obj_hom, flippingIso_inv_toFunctor_map_app_app, Cat.Hom.comp_map, Grothendieck.map_id_eq, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_app_toFunctor_map, 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_mapId_hom_toNatTrans_app_hom_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, Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, Join.pseudofunctorRight_mapId_hom_toNatTrans_app, Limits.fiberwiseColim_map_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, Pseudofunctor.DescentData'.pullHom'₁₃_eq_pullHom_of_chosenPullback₃_assoc, Cat.HasLimits.id_def, Monoidal.whiskerLeft_snd, Limits.fiberwiseColimitLimitIso_inv_app, Bicategory.yoneda_mapId_inv_as_app_toNatTrans_app, CatEnrichedOrdinary.Hom.base_comp, RingCat.moduleCatRestrictScalarsPseudofunctor_mapId, Bicategory.postcomp₂_naturality_hom_toNatTrans_app, 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, Limits.natTransIntoForgetCompFiberwiseColimit_app, ReflQuiv.adj_counit_app, Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_functor_obj_a, hoFunctor.preservesBinaryProducts, Grothendieck.compAsSmallFunctorEquivalence_inverse, Pseudofunctor.StrongTrans.naturality_comp_inv_app, Bicategory.Adj.left_triangle_components, Bicategory.postcomp₂_app_toFunctor_map, Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_inverse_map_hom, Bicategory.precomposingCat_obj, WithInitial.pseudofunctor_mapId, Grothendieck.pre_comp_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, Join.pseudofunctorRight_mapId_inv_toNatTrans_app, Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_counitIso_hom_app_f, RingCat.moduleCatRestrictScalarsPseudofunctor_map, instFullPreordCatPreordToCat, Bicategory.Adj.counit_naturality_assoc, Limits.coconeFiberwiseColimitOfCocone_ι_app, 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, Pseudofunctor.DescentData'.isoMk_hom_hom, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, 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, Bicategory.yoneda₀_mapId_hom_toNatTrans_app, 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, Pseudofunctor.toDescentDataAsCoalgebraCompCoalgebraEquivalenceFunctorIso_hom_app_f, CatEnrichedOrdinary.Hom.comp_eq, Pseudofunctor.ObjectProperty.mapId_hom_app, Grothendieck.ιCompMap_inv_app_base, Pseudofunctor.whiskerLeft_mapId_hom_app, Bicategory.yoneda₀_mapId_inv_toNatTrans_app, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_mapComp_hom_toNatTrans_app, Bicategory.yoneda₀_mapComp_inv_toNatTrans_app, Limits.fiberwiseColimCompEvaluationIso_hom_app, nerve_map, CatEnriched.comp_eq, Cat.Hom.instIsIsoFunctorαCategoryToNatTransInvHom, Pseudofunctor.toDescentData_obj, Cat.Hom.toNatIso_leftUnitor, Pseudofunctor.map₂_whisker_right_app_assoc, Pseudofunctor.DescentDataAsCoalgebra.id_hom, Grothendieck.pre_comp, Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, Bicategory.rightUnitorNatIsoCat_hom_toNatTrans_app, Bicategory.leftUnitorNatIsoCat_inv_toNatTrans_app, Pseudofunctor.presheafHomObjHomEquiv_apply, Cat.Hom.toNatIso_rightUnitor, Pseudofunctor.DescentData'.Hom.comm, Cat.Hom.id_obj, MonCat.toCat_full, curryingIso_inv_toFunctor_obj_obj_obj, Bicategory.postcomposing₂_obj_app_toFunctor_map, Pseudofunctor.mapComp_assoc_right_inv_app_assoc, WithTerminal.pseudofunctor_toPrelaxFunctor, nerveFunctor.full, Grothendieck.functorFrom_obj, LaxFunctor.mapComp_assoc_left_app, Grothendieck.transportIso_inv_fiber, Cat.rightUnitor_inv_app, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str, 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.DescentDataAsCoalgebra.coalgebraEquivalence_unitIso_hom_app_hom, Pseudofunctor.IsStackFor.isEquivalence, Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_inverse_obj_obj, 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, Pseudofunctor.Grothendieck.map_map_fiber, Bicategory.leftUnitorNatIsoCat_hom_toNatTrans_app, Pseudofunctor.map₂_whisker_left_app_assoc, Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, Pseudofunctor.DescentData'.descentDataEquivalence_unitIso, Limits.ι_colimitFiberwiseColimitIso_hom, 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, Functor.leftKanExtensionIsoFiberwiseColimit_hom_app, Pseudofunctor.toDescentData_map_hom, Pseudofunctor.ObjectProperty.IsClosedUnderIsomorphisms.isClosedUnderIsomorphisms, RingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, Cat.freeRefl_obj, Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, Pseudofunctor.DescentData'.pullHom'_hom_self, Pseudofunctor.DescentData.pullFunctorObjHom_eq_assoc, LaxFunctor.map₂_rightUnitor_app_assoc, preordToCat_obj, Functor.elementsFunctor_obj, Pseudofunctor.DescentData'.Hom.comm_assoc, Bicategory.postcomposingCat_map, Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, preordToCat_map, Limits.ι_colimitFiberwiseColimitIso_inv, Codiscrete.adj_unit_app, curryingIso_inv_toFunctor_map_app_app, ReflQuiv.adj.counit.comp_app_eq, Bicategory.yoneda_mapId_hom_as_app_toNatTrans_app, Pseudofunctor.DescentDataAsCoalgebra.comp_hom_assoc, Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, 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, Pseudofunctor.DescentData'.pullHom'_hom_comp, Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_functor_map_f, 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, Pseudofunctor.DescentData'.comm_assoc, 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, Pseudofunctor.DescentData'.pullHom'_self, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, Limits.fiberwiseColimCompEvaluationIso_inv_app, Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq, Grothendieck.functorFrom_map, 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, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_hom_app, Bicategory.associatorNatIsoLeftCat_inv_toNatTrans_app, Limits.coconeOfCoconeFiberwiseColimit_ι_app, Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, Pseudofunctor.mapComp'_id_comp_hom_app, Grothendieck.map_map_fiber, typeToCat_obj, Cat.asSmallFunctor_map, Bicategory.associatorNatIsoMiddleCat_hom_toNatTrans_app, Monoidal.associator_inv, Grothendieck.map_map_base, Monoidal.rightUnitor_inv, Pseudofunctor.DescentDataAsCoalgebra.coassoc, GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_hom_app, 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.DescentDataAsCoalgebra.isoMk_inv_hom, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_app_toFunctor_obj, Pseudofunctor.DescentData.pullFunctorObjHom_eq, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_as_app_toNatTrans_app, Pseudofunctor.DescentDataAsCoalgebra.Hom.comm_assoc, 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, Pseudofunctor.DescentData'.comp_pullHom''_assoc, 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, Pseudofunctor.DescentData'.pullHom'₁₂_eq_pullHom_of_chosenPullback₃_assoc, 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, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, 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, Bicategory.postcomposing₂_obj_app_toFunctor_obj, 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, Pseudofunctor.DescentData'.pullHom'₂₃_eq_pullHom_of_chosenPullback₃_assoc, Cat.whiskerRight_app, LaxFunctor.map₂_associator_app, Grothendieck.congr, Over.mapFunctor_map, Grothendieck.grothendieckTypeToCat_functor_map_coe, Pseudofunctor.DescentData'.pullHom_pullHom'_assoc, Bicategory.yoneda₀_mapComp_hom_toNatTrans_app, CommRingCat.moduleCatRestrictScalarsPseudofunctor_obj, Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, Bicategory.yoneda_mapComp_inv_as_app_toNatTrans_app, Cat.associator_hom_toNatTrans, Cat.Hom.instIsIsoFunctorαCategoryToNatTransHomHom, Bicategory.postcomp₂_naturality_inv_toNatTrans_app, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_obj_map, 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, Pseudofunctor.DescentData'.descentDataEquivalence_counitIso, Pseudofunctor.ObjectProperty.mapComp_inv_app, CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_base, Grothendieck.compAsSmallFunctorEquivalence_counitIso, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_mapId_inv_toNatTrans_app, curryingIso_hom_toFunctor_map_app, Pseudofunctor.DescentData'.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpPullHom'Hom, Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_functor_obj_A, LaxFunctor.mapComp_assoc_right_app_assoc, Pseudofunctor.DescentData'.comp_pullHom'_assoc, instIsIsoSSetProdComparisonCatCompNerveFunctorHoFunctorOf, Grothendieck.grothendieckTypeToCatInverse_obj_fiber_as, nerveAdjunction.isIso_counit, CatEnrichedOrdinary.homEquiv_id, OplaxFunctor.mapComp_naturality_right_app, Cat.instHasColimits, Bicategory.associatorNatIsoMiddleCat_inv_toNatTrans_app, LaxFunctor.mapComp_assoc_left_app_assoc, Pseudofunctor.DescentData'.pullHom'_hom_comp_assoc, Cat.leftUnitor_inv_app, Functor.leftKanExtensionIsoFiberwiseColimit_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.DescentData'.id_hom, Pseudofunctor.CoGrothendieck.compIso_hom_app, Pseudofunctor.DescentData.hom_comp, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_hom_app, 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, Bicategory.rightUnitorNatIsoCat_inv_toNatTrans_app, OplaxFunctor.map₂_rightUnitor_app_assoc, Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_naturality_hom_toNatTrans_app, Pseudofunctor.Grothendieck.map_map_base, Pseudofunctor.DescentDataAsCoalgebra.counit_assoc, Bicategory.postcomposing₂_obj_naturality_inv_toNatTrans_app, Bicategory.associatorNatIsoRightCat_hom_toNatTrans_app, Bicategory.Adj.right_triangle_components_assoc, LaxFunctor.map₂_leftUnitor_app_assoc, Cat.eqToHom_app, Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor, Grothendieck.ι_map, Pseudofunctor.DescentDataAsCoalgebra.isoMk_hom_hom, Pseudofunctor.whiskerRight_mapId_inv_app_assoc, GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_hom_app, Pseudofunctor.StrongTrans.naturality_comp_hom_app, Bicategory.yoneda_mapComp_hom_as_app_toNatTrans_app, Grothendieck.faithful_ι, CatEnrichedOrdinary.Hom.base_id, Pseudofunctor.mapId'_inv_naturality, Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, Pseudofunctor.DescentDataAsCoalgebra.comp_hom, Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_counitIso_inv_app_f, 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

Name	Category	Theorems
chosenTerminal 📖	CompOp	4 math math: 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	33 math math: CategoryTheory.Monoidal.whiskerRight_fst, ihom_obj, CategoryTheory.Monoidal.whiskerRight, SSet.hoFunctor.unitHomEquiv_eq, CategoryTheory.Monoidal.tensorHom, CategoryTheory.CatEnrichedOrdinary.Hom.mk_comp, CategoryTheory.hoFunctor.isIso_prodComparison_of_stdSimplex, 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

Name	Kind	Assumes	Proves	Validates	Depends 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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