Documentation Verification Report

Basic

📁 Source: Mathlib/CategoryTheory/Sums/Basic.lean

Statistics

MetricCount
DefinitionsinlCompSum', inrCompSum', isoSum, sum, sum', sumIsoExt, sum, sum', equivalence, symmetry, homInduction, inl_, inr_, swap, swapCompInl, swapCompInr, sum
17
TheoremsinlCompSum'_hom_app, inlCompSum'_inv_app, inrCompSum'_hom_app, inrCompSum'_inv_app, isoSum_hom_app_inl, isoSum_hom_app_inr, isoSum_inv_app_inl, isoSum_inv_app_inr, sum'_map_inl, sum'_map_inr, sum'_obj_inl, sum'_obj_inr, sumIsoExt_hom_app_inl, sumIsoExt_hom_app_inr, sumIsoExt_inv_app_inl, sumIsoExt_inv_app_inr, sum_map_inl, sum_map_inr, sum_obj_inl, sum_obj_inr, sum'_app_inl, sum'_app_inr, sum_app_inl, sum_app_inr, equivalence_functor, equivalence_inverse, isEquivalence, homInduction_left, homInduction_right, inl__obj, inr__obj, swapCompInl_hom_app, swapCompInl_inv_app, swapCompInr_hom_app, swapCompInr_inv_app, swap_map_inl, swap_map_inr, swap_obj_inl, swap_obj_inr, hom_inl_inr_false, hom_inr_inl_false
41
Total58

CategoryTheory

Definitions

NameCategoryTheorems
sum 📖CompOp
123 mathmath: sum.inrCompInverseAssociator_hom_app, Sum.natTransOfWhiskerLeftInlInr_app, Functor.isoSum_inv_app_inl, Discrete.sumEquiv_counitIso_inv_app, Join.inlCompFromSum_hom_app, sum.associativity_inverse, Sum.functorEquivFunctorCompFstIso_inv_app_app, sum.associator_obj_inr, Discrete.sumEquiv_unitIso_inv_app, Functor.isoSum_inv_app_inr, sum.inlCompInrCompInverseAssociator_hom_app_down_down, Functor.sumIsoExt_hom_app_inl, Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, Sum.functorEquiv_functor_map, sum.inrCompInrCompInverseAssociator_hom_app_down, Functor.inlCompSum'_inv_app, Functor.sum_map_inl, sum.inlCompInrCompInverseAssociator_inv_app_down_down, Sum.Swap.equivalence_inverse, Discrete.sumEquiv_inverse_map, Sum.functorEquiv_unit_app_app_inr, Sum.functorEquiv_unitIso_inv_app_app_inl, sum.associator_map_inr, Join.inrCompFromSum_hom_app, Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, Sum.inl__obj, Sum.functorEquiv_inverse_map, Functor.sum'_map_inr, Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, Functor.sum_obj_inl, Sum.swapCompInl_hom_app, Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, sum.inverseAssociator_map_inr_inr, sum.inverseAssociator_obj_inr_inl, Functor.inlCompSum'_hom_app, Functor.sumIsoExt_inv_app_inr, sum.associatorIsEquivalence, Sum.natTransOfWhiskerLeftInlInr_id, Sum.functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, Join.fromSum_map_inr, sum.inverseAssociatorIsEquivalence, Discrete.sumEquiv_unitIso_hom_app, sum.inverseAssociator_map_inl, Sum.natIsoOfWhiskerLeftInlInr_eq, Functor.sum'_obj_inl, Sum.functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, sum.associativity_functor, Functor.sum'_obj_inr, Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, Functor.sumIsoExt_hom_app_inr, Sum.homInduction_left, Functor.isoSum_hom_app_inl, NatTrans.sum_app_inl, sum.associator_obj_inl_inl, sum.inrCompInrCompInverseAssociator_inv_app_down, Discrete.sumEquiv_counitIso_hom_app, sum.inverseAssociator_obj_inr_inr, sum.inverseAssociator_obj_inl, sum.inlCompAssociator_hom_app, sum.inrCompInlCompAssociator_inv_app_down_down, sum.inlCompInlCompAssociator_inv_app_down, Sum.swap_obj_inl, Sum.Swap.isEquivalence, Functor.sumIsoExt_inv_app_inl, Join.instFaithfulSumFromSum, Sum.homInduction_right, sum.inrCompAssociator_hom_app_down_down, Functor.sum'_map_inl, IsDiscrete.sum, Sum.functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, Discrete.sumEquiv_functor_obj, sum.inrCompInlCompAssociator_hom_app_down_down, Sum.swap_map_inl, Sum.functorEquivFunctorCompSndIso_inv_app_app, Sum.functorEquiv_unitIso_inv_app_app_inr, Sum.swapCompInl_inv_app, Functor.inrCompSum'_inv_app, sum.inrCompAssociator_inv_app_down_down, Sum.swap_map_inr, Sum.natTransOfWhiskerLeftInlInr_comp, Sum.natIsoOfWhiskerLeftInlInr_hom, Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, Sum.swap_obj_inr, Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, Sum.swapCompInr_hom_app, sum.associator_map_inl_inr, sum.inlCompInverseAssociator_inv_app_down_down, sum.associator_obj_inl_inr, Discrete.sumEquiv_inverse_obj, Functor.isoSum_hom_app_inr, Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, Sum.inr__obj, sum.inlCompInlCompAssociator_hom_app_down, Sum.natIsoOfWhiskerLeftInlInr_inv, Join.fromSum_obj, Join.inrCompFromSum_inv_app, Sum.functorEquiv_unit_app_app_inl, Discrete.sumEquiv_functor_map, sum.associator_map_inl_inl, Functor.sum_map_inr, NatTrans.sum'_app_inr, Sum.functorEquiv_inverse_obj, Functor.inrCompSum'_hom_app, NatTrans.sum'_app_inl, Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, Sum.functorEquivFunctorCompSndIso_hom_app_app, Sum.functorEquivFunctorCompFstIso_hom_app_app, sum.inlCompAssociator_inv_app, sum.inverseAssociator_map_inr_inl, Sum.functorEquiv_unitIso, Sum.swapCompInr_inv_app, Join.instEssSurjSumFromSum, Join.fromSum_map_inl, sum.inlCompInverseAssociator_hom_app_down_down, Sum.Swap.equivalence_functor, Functor.sum_obj_inr, sum.inrCompInverseAssociator_inv_app, Join.inlCompFromSum_inv_app, Sum.functorEquiv_counitIso, Sum.functorEquiv_functor_obj, Sum.functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app, NatTrans.sum_app_inr

Theorems

NameKindAssumesProvesValidatesDepends On
hom_inl_inr_false 📖
hom_inr_inl_false 📖

CategoryTheory.Functor

Definitions

NameCategoryTheorems
inlCompSum' 📖CompOp
3 mathmath: inlCompSum'_inv_app, inlCompSum'_hom_app, CategoryTheory.Sum.functorEquiv_counitIso
inrCompSum' 📖CompOp
3 mathmath: inrCompSum'_inv_app, inrCompSum'_hom_app, CategoryTheory.Sum.functorEquiv_counitIso
isoSum 📖CompOp
5 mathmath: isoSum_inv_app_inl, isoSum_inv_app_inr, isoSum_hom_app_inl, isoSum_hom_app_inr, CategoryTheory.Sum.functorEquiv_unitIso
sum 📖CompOp
6 mathmath: sum_map_inl, sum_obj_inl, CategoryTheory.NatTrans.sum_app_inl, sum_map_inr, sum_obj_inr, CategoryTheory.NatTrans.sum_app_inr
sum' 📖CompOp
38 mathmath: CategoryTheory.sum.inrCompInverseAssociator_hom_app, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_app, isoSum_inv_app_inl, CategoryTheory.Discrete.sumEquiv_counitIso_inv_app, CategoryTheory.Join.inlCompFromSum_hom_app, CategoryTheory.Discrete.sumEquiv_unitIso_inv_app, isoSum_inv_app_inr, inlCompSum'_inv_app, CategoryTheory.Join.inrCompFromSum_hom_app, sum'_map_inr, CategoryTheory.Sum.swapCompInl_hom_app, inlCompSum'_hom_app, CategoryTheory.Discrete.sumEquiv_unitIso_hom_app, sum'_obj_inl, sum'_obj_inr, isoSum_hom_app_inl, CategoryTheory.Discrete.sumEquiv_counitIso_hom_app, CategoryTheory.sum.inlCompAssociator_hom_app, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, sum'_map_inl, CategoryTheory.Sum.swapCompInl_inv_app, inrCompSum'_inv_app, CategoryTheory.sum.inrCompAssociator_inv_app_down_down, CategoryTheory.Sum.swapCompInr_hom_app, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, isoSum_hom_app_inr, CategoryTheory.Join.inrCompFromSum_inv_app, CategoryTheory.NatTrans.sum'_app_inr, CategoryTheory.Sum.functorEquiv_inverse_obj, inrCompSum'_hom_app, CategoryTheory.NatTrans.sum'_app_inl, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.Sum.functorEquiv_unitIso, CategoryTheory.Sum.swapCompInr_inv_app, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.sum.inrCompInverseAssociator_inv_app, CategoryTheory.Join.inlCompFromSum_inv_app, CategoryTheory.Sum.functorEquiv_counitIso
sumIsoExt 📖CompOp
4 mathmath: sumIsoExt_hom_app_inl, sumIsoExt_inv_app_inr, sumIsoExt_hom_app_inr, sumIsoExt_inv_app_inl

Theorems

NameKindAssumesProvesValidatesDepends On
inlCompSum'_hom_app 📖mathematicalCategoryTheory.NatTrans.app
comp
CategoryTheory.sum
CategoryTheory.Sum.inl_
sum'
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
inlCompSum'
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
obj
inlCompSum'_inv_app 📖mathematicalCategoryTheory.NatTrans.app
comp
CategoryTheory.sum
CategoryTheory.Sum.inl_
sum'
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
inlCompSum'
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
obj
inrCompSum'_hom_app 📖mathematicalCategoryTheory.NatTrans.app
comp
CategoryTheory.sum
CategoryTheory.Sum.inr_
sum'
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
inrCompSum'
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
obj
inrCompSum'_inv_app 📖mathematicalCategoryTheory.NatTrans.app
comp
CategoryTheory.sum
CategoryTheory.Sum.inr_
sum'
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
inrCompSum'
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
obj
isoSum_hom_app_inl 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
sum'
comp
CategoryTheory.Sum.inl_
CategoryTheory.Sum.inr_
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
isoSum
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
obj
isoSum_hom_app_inr 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
sum'
comp
CategoryTheory.Sum.inl_
CategoryTheory.Sum.inr_
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
isoSum
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
obj
isoSum_inv_app_inl 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
sum'
comp
CategoryTheory.Sum.inl_
CategoryTheory.Sum.inr_
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
isoSum
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
obj
isoSum_inv_app_inr 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
sum'
comp
CategoryTheory.Sum.inl_
CategoryTheory.Sum.inr_
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
isoSum
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
obj
sum'_map_inl 📖mathematicalmap
CategoryTheory.sum
sum'
obj
CategoryTheory.Sum.inl_
sum'_map_inr 📖mathematicalmap
CategoryTheory.sum
sum'
obj
CategoryTheory.Sum.inr_
sum'_obj_inl 📖mathematicalobj
CategoryTheory.sum
sum'
sum'_obj_inr 📖mathematicalobj
CategoryTheory.sum
sum'
sumIsoExt_hom_app_inl 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
sumIsoExt
comp
CategoryTheory.Sum.inl_
sumIsoExt_hom_app_inr 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
CategoryTheory.Iso.hom
CategoryTheory.Functor
category
sumIsoExt
comp
CategoryTheory.Sum.inr_
sumIsoExt_inv_app_inl 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
sumIsoExt
comp
CategoryTheory.Sum.inl_
sumIsoExt_inv_app_inr 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
CategoryTheory.Iso.inv
CategoryTheory.Functor
category
sumIsoExt
comp
CategoryTheory.Sum.inr_
sum_map_inl 📖mathematicalmap
CategoryTheory.sum
sum
obj
CategoryTheory.Sum.inl_
sum_map_inr 📖mathematicalmap
CategoryTheory.sum
sum
obj
CategoryTheory.Sum.inr_
sum_obj_inl 📖mathematicalobj
CategoryTheory.sum
sum
sum_obj_inr 📖mathematicalobj
CategoryTheory.sum
sum

CategoryTheory.NatTrans

Definitions

NameCategoryTheorems
sum 📖CompOp
2 mathmath: sum_app_inl, sum_app_inr
sum' 📖CompOp
6 mathmath: CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_app, CategoryTheory.Sum.functorEquiv_inverse_map, sum'_app_inr, sum'_app_inl, CategoryTheory.Sum.functorEquiv_unitIso, CategoryTheory.Sum.functorEquiv_counitIso

Theorems

NameKindAssumesProvesValidatesDepends On
sum'_app_inl 📖mathematicalapp
CategoryTheory.sum
CategoryTheory.Functor.sum'
sum'
sum'_app_inr 📖mathematicalapp
CategoryTheory.sum
CategoryTheory.Functor.sum'
sum'
sum_app_inl 📖mathematicalapp
CategoryTheory.sum
CategoryTheory.Functor.sum
sum
CategoryTheory.Functor.map
CategoryTheory.Sum.inl_
CategoryTheory.Functor.obj
sum_app_inr 📖mathematicalapp
CategoryTheory.sum
CategoryTheory.Functor.sum
sum
CategoryTheory.Functor.map
CategoryTheory.Sum.inr_
CategoryTheory.Functor.obj

CategoryTheory.Sum

Definitions

NameCategoryTheorems
homInduction 📖CompOp
3 mathmath: CategoryTheory.Discrete.sumEquiv_inverse_map, homInduction_left, homInduction_right
inl_ 📖CompOp
60 mathmath: CategoryTheory.sum.inrCompInverseAssociator_hom_app, natTransOfWhiskerLeftInlInr_app, CategoryTheory.Functor.isoSum_inv_app_inl, CategoryTheory.Join.inlCompFromSum_hom_app, functorEquivFunctorCompFstIso_inv_app_app, CategoryTheory.Functor.isoSum_inv_app_inr, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, CategoryTheory.Functor.sumIsoExt_hom_app_inl, associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, functorEquiv_functor_map, CategoryTheory.Functor.inlCompSum'_inv_app, CategoryTheory.Functor.sum_map_inl, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, inl__obj, Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, swapCompInl_hom_app, CategoryTheory.Functor.inlCompSum'_hom_app, natTransOfWhiskerLeftInlInr_id, CategoryTheory.sum.inverseAssociator_map_inl, natIsoOfWhiskerLeftInlInr_eq, functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, homInduction_left, CategoryTheory.Functor.isoSum_hom_app_inl, CategoryTheory.NatTrans.sum_app_inl, CategoryTheory.sum.inlCompAssociator_hom_app, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, CategoryTheory.Functor.sumIsoExt_inv_app_inl, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.Functor.sum'_map_inl, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, swapCompInl_inv_app, CategoryTheory.sum.inrCompAssociator_inv_app_down_down, natTransOfWhiskerLeftInlInr_comp, natIsoOfWhiskerLeftInlInr_hom, associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, swapCompInr_hom_app, CategoryTheory.sum.associator_map_inl_inr, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, CategoryTheory.Functor.isoSum_hom_app_inr, Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, natIsoOfWhiskerLeftInlInr_inv, CategoryTheory.sum.associator_map_inl_inl, associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, functorEquivFunctorCompFstIso_hom_app_app, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.sum.inverseAssociator_map_inr_inl, functorEquiv_unitIso, swapCompInr_inv_app, CategoryTheory.Join.fromSum_map_inl, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.sum.inrCompInverseAssociator_inv_app, CategoryTheory.Join.inlCompFromSum_inv_app, functorEquiv_counitIso, functorEquiv_functor_obj, functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app
inr_ 📖CompOp
60 mathmath: CategoryTheory.sum.inrCompInverseAssociator_hom_app, natTransOfWhiskerLeftInlInr_app, CategoryTheory.Functor.isoSum_inv_app_inl, CategoryTheory.Functor.isoSum_inv_app_inr, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, functorEquiv_functor_map, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.sum.associator_map_inr, CategoryTheory.Join.inrCompFromSum_hom_app, Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, CategoryTheory.Functor.sum'_map_inr, Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, swapCompInl_hom_app, associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, CategoryTheory.sum.inverseAssociator_map_inr_inr, CategoryTheory.Functor.sumIsoExt_inv_app_inr, natTransOfWhiskerLeftInlInr_id, functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, CategoryTheory.Join.fromSum_map_inr, natIsoOfWhiskerLeftInlInr_eq, CategoryTheory.Functor.sumIsoExt_hom_app_inr, CategoryTheory.Functor.isoSum_hom_app_inl, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, CategoryTheory.sum.inlCompAssociator_hom_app, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, homInduction_right, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, functorEquivFunctorCompSndIso_inv_app_app, swapCompInl_inv_app, CategoryTheory.Functor.inrCompSum'_inv_app, CategoryTheory.sum.inrCompAssociator_inv_app_down_down, natTransOfWhiskerLeftInlInr_comp, natIsoOfWhiskerLeftInlInr_hom, associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, swapCompInr_hom_app, CategoryTheory.sum.associator_map_inl_inr, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, CategoryTheory.Functor.isoSum_hom_app_inr, Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, inr__obj, natIsoOfWhiskerLeftInlInr_inv, CategoryTheory.Join.inrCompFromSum_inv_app, CategoryTheory.Functor.sum_map_inr, CategoryTheory.Functor.inrCompSum'_hom_app, functorEquivFunctorCompSndIso_hom_app_app, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.sum.inverseAssociator_map_inr_inl, functorEquiv_unitIso, swapCompInr_inv_app, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.sum.inrCompInverseAssociator_inv_app, functorEquiv_counitIso, functorEquiv_functor_obj, CategoryTheory.NatTrans.sum_app_inr
swap 📖CompOp
15 mathmath: Swap.equivalence_inverse, Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, swapCompInl_hom_app, swap_obj_inl, Swap.isEquivalence, swap_map_inl, swapCompInl_inv_app, swap_map_inr, swap_obj_inr, Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, swapCompInr_hom_app, Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, swapCompInr_inv_app, Swap.equivalence_functor
swapCompInl 📖CompOp
4 mathmath: Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, swapCompInl_hom_app, swapCompInl_inv_app, Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst
swapCompInr 📖CompOp
4 mathmath: Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, swapCompInr_hom_app, Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, swapCompInr_inv_app

Theorems

NameKindAssumesProvesValidatesDepends On
homInduction_left 📖mathematicalhomInduction
CategoryTheory.Functor.obj
CategoryTheory.sum
inl_
CategoryTheory.Functor.map
homInduction_right 📖mathematicalhomInduction
CategoryTheory.Functor.obj
CategoryTheory.sum
inr_
CategoryTheory.Functor.map
inl__obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.sum
inl_
inr__obj 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.sum
inr_
swapCompInl_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
CategoryTheory.Functor.comp
inl_
CategoryTheory.Functor.sum'
inr_
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
swap
swapCompInl
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
swapCompInl_inv_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
inr_
CategoryTheory.Functor.comp
inl_
CategoryTheory.Functor.sum'
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
swap
swapCompInl
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
swapCompInr_hom_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
CategoryTheory.Functor.comp
inr_
CategoryTheory.Functor.sum'
inl_
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
swap
swapCompInr
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
swapCompInr_inv_app 📖mathematicalCategoryTheory.NatTrans.app
CategoryTheory.sum
inl_
CategoryTheory.Functor.comp
inr_
CategoryTheory.Functor.sum'
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
swap
swapCompInr
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
swap_map_inl 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.sum
swap
swap_map_inr 📖mathematicalCategoryTheory.Functor.map
CategoryTheory.sum
swap
swap_obj_inl 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.sum
swap
swap_obj_inr 📖mathematicalCategoryTheory.Functor.obj
CategoryTheory.sum
swap

CategoryTheory.Sum.Swap

Definitions

NameCategoryTheorems
equivalence 📖CompOp
6 mathmath: equivalence_inverse, equivalenceFunctorEquivFunctorIso_inv_app_fst, equivalenceFunctorEquivFunctorIso_hom_app_snd, equivalenceFunctorEquivFunctorIso_hom_app_fst, equivalenceFunctorEquivFunctorIso_inv_app_snd, equivalence_functor
symmetry 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
equivalence_functor 📖mathematicalCategoryTheory.Equivalence.functor
CategoryTheory.sum
equivalence
CategoryTheory.Sum.swap
equivalence_inverse 📖mathematicalCategoryTheory.Equivalence.inverse
CategoryTheory.sum
equivalence
CategoryTheory.Sum.swap
isEquivalence 📖mathematicalCategoryTheory.Functor.IsEquivalence
CategoryTheory.sum
CategoryTheory.Sum.swap
CategoryTheory.Equivalence.isEquivalence_functor

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