Documentation Verification Report

Adj

📁 Source: Mathlib/CategoryTheory/Bicategory/Adjunction/Adj.lean

Statistics

MetricCount
DefinitionsAdj, associator, leftUnitor, rightUnitor, whiskerLeft, whiskerRight, adj, l, r, Hom₂, τl, τr, forget₁, inst, instCategoryHom, instCategoryStruct, instCategoryStructHom, iso₂Mk, lIso, obj, rIso, Adj, Adj, Adj, Adj
25
Theoremsassociator_hom_τl, associator_hom_τr, associator_inv_τl, associator_inv_τr, leftUnitor_hom_τl, leftUnitor_hom_τr, leftUnitor_inv_τl, leftUnitor_inv_τr, rightUnitor_hom_τl, rightUnitor_hom_τr, rightUnitor_inv_τl, rightUnitor_inv_τr, whiskerLeft_τl, whiskerLeft_τr, whiskerRight_τl, whiskerRight_τr, conjugateEquiv_symm_τr, conjugateEquiv_τl, ext, ext_iff, associator_hom_τl, associator_hom_τr, associator_inv_τl, associator_inv_τr, comp_adj, comp_l, comp_r, comp_τl, comp_τl_assoc, comp_τr, comp_τr_assoc, forget₁_mapComp, forget₁_mapId, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, hom₂_ext, hom₂_ext_iff, id_adj, id_l, id_r, id_τl, id_τr, iso₂Mk_hom_τl, iso₂Mk_hom_τr, iso₂Mk_inv_τl, iso₂Mk_inv_τr, lIso_hom, lIso_inv, leftUnitor_hom_τl, leftUnitor_hom_τr, leftUnitor_inv_τl, leftUnitor_inv_τr, mk_obj, rIso_hom, rIso_inv, rightUnitor_hom_τl, rightUnitor_hom_τr, rightUnitor_inv_τl, rightUnitor_inv_τr, whiskerLeft_τl, whiskerLeft_τr, whiskerRight_τl, whiskerRight_τr
64
Total89

CategoryTheory.Bicategory

Definitions

NameCategoryTheorems
Adj 📖CompData
69 mathmath: AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_adj, Adj.rightUnitor_hom_τl, Adj.comp_r, Adj.associator_inv_τr, Adj.rIso_inv, Adj.comp_τl_assoc, Adj.forget₁_mapId, Adj.Bicategory.rightUnitor_inv_τr, Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_l, Adj.Bicategory.rightUnitor_inv_τl, Adj.Bicategory.whiskerRight_τl, Adj.rightUnitor_inv_τl, Adj.rightUnitor_hom_τr, Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, Adj.Bicategory.rightUnitor_hom_τr, Adj.id_τl, Adj.comp_τl, Adj.Bicategory.whiskerLeft_τr, Adj.Bicategory.whiskerLeft_τl, Adj.id_τr, Adj.iso₂Mk_inv_τl, Adj.Bicategory.leftUnitor_hom_τl, Adj.whiskerRight_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, Adj.Bicategory.rightUnitor_hom_τl, Adj.Bicategory.leftUnitor_inv_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, Adj.iso₂Mk_hom_τl, Adj.leftUnitor_inv_τl, Adj.whiskerLeft_τr, Adj.id_adj, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, Adj.comp_τr_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_obj_obj, Adj.iso₂Mk_hom_τr, Adj.whiskerRight_τl, Adj.rIso_hom, Adj.rightUnitor_inv_τr, Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, Adj.Bicategory.leftUnitor_hom_τr, Adj.id_l, Adj.Bicategory.associator_inv_τl, Adj.whiskerLeft_τl, Adj.id_r, Adj.associator_inv_τl, Adj.comp_τr, Adj.lIso_inv, Adj.comp_adj, Adj.Bicategory.associator_hom_τr, Adj.associator_hom_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, Adj.leftUnitor_inv_τr, Adj.Bicategory.associator_inv_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, Adj.associator_hom_τl, Adj.Bicategory.whiskerRight_τr, Adj.comp_l, Adj.iso₂Mk_inv_τr, Adj.leftUnitor_hom_τr, Adj.lIso_hom, Adj.Bicategory.associator_hom_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_r, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, Adj.forget₁_mapComp, Adj.Bicategory.leftUnitor_inv_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, Adj.leftUnitor_hom_τl

CategoryTheory.Bicategory.Adj

Definitions

NameCategoryTheorems
Hom₂ 📖CompData
forget₁ 📖CompOp
5 mathmath: forget₁_mapId, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, forget₁_mapComp
inst 📖CompOp
33 mathmath: AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_adj, rightUnitor_hom_τl, associator_inv_τr, forget₁_mapId, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_l, rightUnitor_inv_τl, rightUnitor_hom_τr, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, whiskerRight_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, leftUnitor_inv_τl, whiskerLeft_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_obj_obj, whiskerRight_τl, rightUnitor_inv_τr, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, whiskerLeft_τl, associator_inv_τl, associator_hom_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, leftUnitor_inv_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, associator_hom_τl, leftUnitor_hom_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_r, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, forget₁_mapComp, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, leftUnitor_hom_τl
instCategoryHom 📖CompOp
40 mathmath: rightUnitor_hom_τl, associator_inv_τr, rIso_inv, Bicategory.rightUnitor_inv_τr, Bicategory.rightUnitor_inv_τl, rightUnitor_inv_τl, rightUnitor_hom_τr, Bicategory.rightUnitor_hom_τr, iso₂Mk_inv_τl, Bicategory.leftUnitor_hom_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, Bicategory.rightUnitor_hom_τl, Bicategory.leftUnitor_inv_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, iso₂Mk_hom_τl, leftUnitor_inv_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, iso₂Mk_hom_τr, rIso_hom, rightUnitor_inv_τr, Bicategory.leftUnitor_hom_τr, Bicategory.associator_inv_τl, associator_inv_τl, lIso_inv, Bicategory.associator_hom_τr, associator_hom_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, leftUnitor_inv_τr, Bicategory.associator_inv_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, associator_hom_τl, iso₂Mk_inv_τr, leftUnitor_hom_τr, lIso_hom, Bicategory.associator_hom_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, Bicategory.leftUnitor_inv_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, leftUnitor_hom_τl
instCategoryStruct 📖CompOp
60 mathmath: rightUnitor_hom_τl, comp_r, associator_inv_τr, rIso_inv, comp_τl_assoc, Bicategory.rightUnitor_inv_τr, Bicategory.rightUnitor_inv_τl, Bicategory.whiskerRight_τl, rightUnitor_inv_τl, rightUnitor_hom_τr, Bicategory.rightUnitor_hom_τr, id_τl, comp_τl, Bicategory.whiskerLeft_τr, Bicategory.whiskerLeft_τl, id_τr, iso₂Mk_inv_τl, Bicategory.leftUnitor_hom_τl, whiskerRight_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, Bicategory.rightUnitor_hom_τl, Bicategory.leftUnitor_inv_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, iso₂Mk_hom_τl, leftUnitor_inv_τl, whiskerLeft_τr, id_adj, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, comp_τr_assoc, iso₂Mk_hom_τr, whiskerRight_τl, rIso_hom, rightUnitor_inv_τr, Bicategory.leftUnitor_hom_τr, id_l, Bicategory.associator_inv_τl, whiskerLeft_τl, id_r, associator_inv_τl, comp_τr, lIso_inv, comp_adj, Bicategory.associator_hom_τr, associator_hom_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, leftUnitor_inv_τr, Bicategory.associator_inv_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, associator_hom_τl, Bicategory.whiskerRight_τr, comp_l, iso₂Mk_inv_τr, leftUnitor_hom_τr, lIso_hom, Bicategory.associator_hom_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, Bicategory.leftUnitor_inv_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, leftUnitor_hom_τl
instCategoryStructHom 📖CompOp
6 mathmath: comp_τl_assoc, id_τl, comp_τl, id_τr, comp_τr_assoc, comp_τr
iso₂Mk 📖CompOp
4 mathmath: iso₂Mk_inv_τl, iso₂Mk_hom_τl, iso₂Mk_hom_τr, iso₂Mk_inv_τr
lIso 📖CompOp
2 mathmath: lIso_inv, lIso_hom
obj 📖CompOp
59 mathmath: AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_adj, rightUnitor_hom_τl, comp_r, associator_inv_τr, rIso_inv, comp_τl_assoc, forget₁_mapId, Bicategory.rightUnitor_inv_τr, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_l, Bicategory.rightUnitor_inv_τl, Bicategory.whiskerRight_τl, rightUnitor_inv_τl, Hom₂.conjugateEquiv_symm_τr, rightUnitor_hom_τr, forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, Bicategory.rightUnitor_hom_τr, id_τl, comp_τl, Bicategory.whiskerLeft_τr, Bicategory.whiskerLeft_τl, id_τr, Bicategory.leftUnitor_hom_τl, whiskerRight_τr, Bicategory.rightUnitor_hom_τl, Bicategory.leftUnitor_inv_τl, leftUnitor_inv_τl, whiskerLeft_τr, id_adj, comp_τr_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_obj_obj, whiskerRight_τl, rIso_hom, rightUnitor_inv_τr, Bicategory.leftUnitor_hom_τr, id_l, Bicategory.associator_inv_τl, whiskerLeft_τl, id_r, Hom₂.conjugateEquiv_τl, associator_inv_τl, comp_τr, lIso_inv, comp_adj, Bicategory.associator_hom_τr, associator_hom_τr, leftUnitor_inv_τr, Bicategory.associator_inv_τr, mk_obj, associator_hom_τl, Bicategory.whiskerRight_τr, comp_l, leftUnitor_hom_τr, lIso_hom, Bicategory.associator_hom_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_r, forget₁_mapComp, Bicategory.leftUnitor_inv_τr, leftUnitor_hom_τl
rIso 📖CompOp
2 mathmath: rIso_inv, rIso_hom

Theorems

NameKindAssumesProvesValidatesDepends On
associator_hom_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.associator
inst
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
associator_hom_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.associator
inst
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.r
associator_inv_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.associator
inst
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
associator_inv_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.associator
inst
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.r
comp_adj 📖mathematicalHom.adj
obj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.Adjunction.comp
Hom.l
Hom.r
comp_l 📖mathematicalHom.l
obj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.toCategoryStruct
comp_r 📖mathematicalHom.r
obj
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.toCategoryStruct
comp_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.comp
Quiver.Hom
CategoryTheory.Bicategory.Adj
CategoryTheory.CategoryStruct.toQuiver
instCategoryStruct
instCategoryStructHom
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.l
comp_τl_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.l
Hom₂.τl
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryStructHom
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_τl
comp_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.comp
Quiver.Hom
CategoryTheory.Bicategory.Adj
CategoryTheory.CategoryStruct.toQuiver
instCategoryStruct
instCategoryStructHom
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.r
comp_τr_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.r
Hom₂.τr
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryStructHom
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_τr
forget₁_mapComp 📖mathematicalCategoryTheory.Pseudofunctor.mapComp
CategoryTheory.Bicategory.Adj
inst
forget₁
CategoryTheory.Iso.refl
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
CategoryTheory.CategoryStruct.comp
forget₁_mapId 📖mathematicalCategoryTheory.Pseudofunctor.mapId
CategoryTheory.Bicategory.Adj
inst
forget₁
CategoryTheory.Iso.refl
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
CategoryTheory.CategoryStruct.id
forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_map₂ 📖mathematicalCategoryTheory.PrelaxFunctorStruct.map₂
CategoryTheory.Bicategory.Adj
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
inst
Quiver.Hom
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct
CategoryTheory.Pseudofunctor.toPrelaxFunctor
forget₁
Hom₂.τl
forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map 📖mathematicalPrefunctor.map
CategoryTheory.Bicategory.Adj
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
inst
CategoryTheory.PrelaxFunctorStruct.toPrefunctor
Quiver.Hom
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct
CategoryTheory.Pseudofunctor.toPrelaxFunctor
forget₁
Hom.l
obj
forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj 📖mathematicalPrefunctor.obj
CategoryTheory.Bicategory.Adj
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
inst
CategoryTheory.PrelaxFunctorStruct.toPrefunctor
Quiver.Hom
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct
CategoryTheory.Pseudofunctor.toPrelaxFunctor
forget₁
obj
hom₂_ext 📖Hom₂.τlHom₂.ext
hom₂_ext_iff 📖mathematicalHom₂.τlhom₂_ext
id_adj 📖mathematicalHom.adj
obj
CategoryTheory.CategoryStruct.id
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.Adjunction.id
id_l 📖mathematicalHom.l
obj
CategoryTheory.CategoryStruct.id
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.toCategoryStruct
id_r 📖mathematicalHom.r
obj
CategoryTheory.CategoryStruct.id
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.toCategoryStruct
id_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.id
Quiver.Hom
CategoryTheory.Bicategory.Adj
CategoryTheory.CategoryStruct.toQuiver
instCategoryStruct
instCategoryStructHom
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.l
id_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.id
Quiver.Hom
CategoryTheory.Bicategory.Adj
CategoryTheory.CategoryStruct.toQuiver
instCategoryStruct
instCategoryStructHom
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.r
iso₂Mk_hom_τl 📖mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.r
DFunLike.coe
Equiv
Hom.l
EquivLike.toFunLike
Equiv.instEquivLike
CategoryTheory.Bicategory.conjugateEquiv
Hom.adj
CategoryTheory.Iso.hom
Hom₂.τl
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryHom
iso₂Mk
iso₂Mk_hom_τr 📖mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.r
DFunLike.coe
Equiv
Hom.l
EquivLike.toFunLike
Equiv.instEquivLike
CategoryTheory.Bicategory.conjugateEquiv
Hom.adj
CategoryTheory.Iso.hom
Hom₂.τr
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryHom
iso₂Mk
iso₂Mk_inv_τl 📖mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.r
DFunLike.coe
Equiv
Hom.l
EquivLike.toFunLike
Equiv.instEquivLike
CategoryTheory.Bicategory.conjugateEquiv
Hom.adj
CategoryTheory.Iso.hom
Hom₂.τl
CategoryTheory.Iso.inv
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryHom
iso₂Mk
iso₂Mk_inv_τr 📖mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
Hom.r
DFunLike.coe
Equiv
Hom.l
EquivLike.toFunLike
Equiv.instEquivLike
CategoryTheory.Bicategory.conjugateEquiv
Hom.adj
CategoryTheory.Iso.hom
Hom₂.τr
CategoryTheory.Iso.inv
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryHom
iso₂Mk
lIso_hom 📖mathematicalCategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
lIso
Hom₂.τl
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryHom
lIso_inv 📖mathematicalCategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
lIso
Hom₂.τl
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryHom
leftUnitor_hom_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.leftUnitor
inst
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
leftUnitor_hom_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.leftUnitor
inst
CategoryTheory.Iso.inv
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.r
CategoryTheory.Bicategory.rightUnitor
leftUnitor_inv_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.leftUnitor
inst
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
leftUnitor_inv_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.leftUnitor
inst
CategoryTheory.Iso.hom
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.r
CategoryTheory.Bicategory.rightUnitor
mk_obj 📖mathematicalobj
rIso_hom 📖mathematicalCategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.r
rIso
Hom₂.τr
CategoryTheory.Iso.inv
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryHom
rIso_inv 📖mathematicalCategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.r
rIso
Hom₂.τr
CategoryTheory.Iso.hom
CategoryTheory.Bicategory.Adj
instCategoryStruct
instCategoryHom
rightUnitor_hom_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.rightUnitor
inst
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
rightUnitor_hom_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.rightUnitor
inst
CategoryTheory.Iso.inv
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.r
CategoryTheory.Bicategory.leftUnitor
rightUnitor_inv_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.rightUnitor
inst
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.l
rightUnitor_inv_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
instCategoryHom
CategoryTheory.Bicategory.rightUnitor
inst
CategoryTheory.Iso.hom
CategoryTheory.Bicategory.toCategoryStruct
obj
CategoryTheory.Bicategory.homCategory
Hom.r
CategoryTheory.Bicategory.leftUnitor
whiskerLeft_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.whiskerLeft
inst
obj
Hom.l
whiskerLeft_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.whiskerLeft
inst
CategoryTheory.Bicategory.whiskerRight
obj
Hom.r
whiskerRight_τl 📖mathematicalHom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.whiskerRight
inst
obj
Hom.l
whiskerRight_τr 📖mathematicalHom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
instCategoryStruct
CategoryTheory.Bicategory.whiskerRight
inst
CategoryTheory.Bicategory.whiskerLeft
obj
Hom.r

CategoryTheory.Bicategory.Adj.Bicategory

Definitions

NameCategoryTheorems
associator 📖CompOp
4 mathmath: associator_inv_τl, associator_hom_τr, associator_inv_τr, associator_hom_τl
leftUnitor 📖CompOp
4 mathmath: leftUnitor_hom_τl, leftUnitor_inv_τl, leftUnitor_hom_τr, leftUnitor_inv_τr
rightUnitor 📖CompOp
4 mathmath: rightUnitor_inv_τr, rightUnitor_inv_τl, rightUnitor_hom_τr, rightUnitor_hom_τl
whiskerLeft 📖CompOp
2 mathmath: whiskerLeft_τr, whiskerLeft_τl
whiskerRight 📖CompOp
2 mathmath: whiskerRight_τl, whiskerRight_τr

Theorems

NameKindAssumesProvesValidatesDepends On
associator_hom_τl 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
associator
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.l
CategoryTheory.Bicategory.associator
associator_hom_τr 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
associator
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.r
CategoryTheory.Bicategory.associator
associator_inv_τl 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
associator
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.l
CategoryTheory.Bicategory.associator
associator_inv_τr 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
associator
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.r
CategoryTheory.Bicategory.associator
leftUnitor_hom_τl 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
leftUnitor
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.l
CategoryTheory.Bicategory.leftUnitor
leftUnitor_hom_τr 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
leftUnitor
CategoryTheory.Iso.inv
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.r
CategoryTheory.Bicategory.rightUnitor
leftUnitor_inv_τl 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
leftUnitor
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.l
CategoryTheory.Bicategory.leftUnitor
leftUnitor_inv_τr 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
leftUnitor
CategoryTheory.Iso.hom
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.r
CategoryTheory.Bicategory.rightUnitor
rightUnitor_hom_τl 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
rightUnitor
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.l
CategoryTheory.Bicategory.rightUnitor
rightUnitor_hom_τr 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
rightUnitor
CategoryTheory.Iso.inv
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.r
CategoryTheory.Bicategory.leftUnitor
rightUnitor_inv_τl 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
rightUnitor
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.l
CategoryTheory.Bicategory.rightUnitor
rightUnitor_inv_τr 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.Adj.instCategoryHom
rightUnitor
CategoryTheory.Iso.hom
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.r
CategoryTheory.Bicategory.leftUnitor
whiskerLeft_τl 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
whiskerLeft
CategoryTheory.Bicategory.whiskerLeft
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.Adj.Hom.l
whiskerLeft_τr 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
whiskerLeft
CategoryTheory.Bicategory.whiskerRight
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.Adj.Hom.r
whiskerRight_τl 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τl
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
whiskerRight
CategoryTheory.Bicategory.whiskerRight
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.Adj.Hom.l
whiskerRight_τr 📖mathematicalCategoryTheory.Bicategory.Adj.Hom₂.τr
CategoryTheory.CategoryStruct.comp
CategoryTheory.Bicategory.Adj
CategoryTheory.Bicategory.Adj.instCategoryStruct
whiskerRight
CategoryTheory.Bicategory.whiskerLeft
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Bicategory.Adj.Hom.r

CategoryTheory.Bicategory.Adj.Hom

Definitions

NameCategoryTheorems
adj 📖CompOp
5 mathmath: AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_adj, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_symm_τr, CategoryTheory.Bicategory.Adj.id_adj, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_τl, CategoryTheory.Bicategory.Adj.comp_adj
l 📖CompOp
30 mathmath: CategoryTheory.Bicategory.Adj.rightUnitor_hom_τl, CategoryTheory.Bicategory.Adj.comp_τl_assoc, CategoryTheory.Bicategory.Adj.forget₁_mapId, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_l, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τl, CategoryTheory.Bicategory.Adj.Bicategory.whiskerRight_τl, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τl, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_symm_τr, CategoryTheory.Bicategory.Adj.id_τl, CategoryTheory.Bicategory.Adj.comp_τl, CategoryTheory.Bicategory.Adj.Bicategory.whiskerLeft_τl, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τl, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τl, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τl, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τl, CategoryTheory.Bicategory.Adj.whiskerRight_τl, CategoryTheory.Bicategory.Adj.id_l, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τl, CategoryTheory.Bicategory.Adj.whiskerLeft_τl, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_τl, CategoryTheory.Bicategory.Adj.associator_inv_τl, CategoryTheory.Bicategory.Adj.lIso_inv, CategoryTheory.Bicategory.Adj.comp_adj, CategoryTheory.Bicategory.Adj.associator_hom_τl, CategoryTheory.Bicategory.Adj.comp_l, CategoryTheory.Bicategory.Adj.lIso_hom, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τl, CategoryTheory.Bicategory.Adj.forget₁_mapComp, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τl
r 📖CompOp
27 mathmath: CategoryTheory.Bicategory.Adj.comp_r, CategoryTheory.Bicategory.Adj.associator_inv_τr, CategoryTheory.Bicategory.Adj.rIso_inv, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τr, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_symm_τr, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τr, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τr, CategoryTheory.Bicategory.Adj.Bicategory.whiskerLeft_τr, CategoryTheory.Bicategory.Adj.id_τr, CategoryTheory.Bicategory.Adj.whiskerRight_τr, CategoryTheory.Bicategory.Adj.whiskerLeft_τr, CategoryTheory.Bicategory.Adj.comp_τr_assoc, CategoryTheory.Bicategory.Adj.rIso_hom, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τr, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τr, CategoryTheory.Bicategory.Adj.id_r, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_τl, CategoryTheory.Bicategory.Adj.comp_τr, CategoryTheory.Bicategory.Adj.comp_adj, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τr, CategoryTheory.Bicategory.Adj.associator_hom_τr, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τr, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τr, CategoryTheory.Bicategory.Adj.Bicategory.whiskerRight_τr, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_r, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τr

CategoryTheory.Bicategory.Adj.Hom₂

Definitions

NameCategoryTheorems
τl 📖CompOp
32 mathmath: CategoryTheory.Bicategory.Adj.rightUnitor_hom_τl, CategoryTheory.Bicategory.Adj.comp_τl_assoc, CategoryTheory.Bicategory.Adj.hom₂_ext_iff, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τl, CategoryTheory.Bicategory.Adj.Bicategory.whiskerRight_τl, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τl, conjugateEquiv_symm_τr, CategoryTheory.Bicategory.Adj.id_τl, CategoryTheory.Bicategory.Adj.comp_τl, CategoryTheory.Bicategory.Adj.Bicategory.whiskerLeft_τl, CategoryTheory.Bicategory.Adj.iso₂Mk_inv_τl, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τl, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τl, CategoryTheory.Bicategory.Adj.iso₂Mk_hom_τl, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τl, CategoryTheory.Bicategory.Adj.whiskerRight_τl, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τl, CategoryTheory.Bicategory.Adj.whiskerLeft_τl, conjugateEquiv_τl, CategoryTheory.Bicategory.Adj.associator_inv_τl, CategoryTheory.Bicategory.Adj.lIso_inv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, ext_iff, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, CategoryTheory.Bicategory.Adj.associator_hom_τl, CategoryTheory.Bicategory.Adj.lIso_hom, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τl, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τl
τr 📖CompOp
30 mathmath: CategoryTheory.Bicategory.Adj.associator_inv_τr, CategoryTheory.Bicategory.Adj.rIso_inv, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τr, conjugateEquiv_symm_τr, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τr, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τr, CategoryTheory.Bicategory.Adj.Bicategory.whiskerLeft_τr, CategoryTheory.Bicategory.Adj.id_τr, CategoryTheory.Bicategory.Adj.whiskerRight_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, CategoryTheory.Bicategory.Adj.whiskerLeft_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, CategoryTheory.Bicategory.Adj.comp_τr_assoc, CategoryTheory.Bicategory.Adj.iso₂Mk_hom_τr, CategoryTheory.Bicategory.Adj.rIso_hom, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τr, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τr, conjugateEquiv_τl, CategoryTheory.Bicategory.Adj.comp_τr, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τr, CategoryTheory.Bicategory.Adj.associator_hom_τr, ext_iff, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τr, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τr, CategoryTheory.Bicategory.Adj.Bicategory.whiskerRight_τr, CategoryTheory.Bicategory.Adj.iso₂Mk_inv_τr, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τr, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr

Theorems

NameKindAssumesProvesValidatesDepends On
conjugateEquiv_symm_τr 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.r
CategoryTheory.Bicategory.Adj.Hom.l
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
CategoryTheory.Bicategory.conjugateEquiv
CategoryTheory.Bicategory.Adj.Hom.adj
τr
τl
conjugateEquiv_τl
Equiv.symm_apply_apply
conjugateEquiv_τl 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Bicategory.toCategoryStruct
CategoryTheory.Bicategory.Adj.obj
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Bicategory.homCategory
CategoryTheory.Bicategory.Adj.Hom.l
CategoryTheory.Bicategory.Adj.Hom.r
EquivLike.toFunLike
Equiv.instEquivLike
CategoryTheory.Bicategory.conjugateEquiv
CategoryTheory.Bicategory.Adj.Hom.adj
τl
τr
ext 📖τl
τr
ext_iff 📖mathematicalτl
τr
ext

Digraph

Definitions

NameCategoryTheorems
Adj 📖MathDef
15 mathmath: adj_inj, sup_adj, bot_adj, completeBipartiteGraph_Adj, inf_adj, sdiff_adj, iSup_adj, top_adj, sInf_adj, sSup_adj, compl_adj, adj_injective, iInf_adj, mk'_apply_Adj, ext_iff

Graph

Definitions

NameCategoryTheorems
Adj 📖MathDef
2 mathmath: IsLink.adj, adj_comm

SimpleGraph

Definitions

NameCategoryTheorems
Adj 📖MathDef
307 mathmath: adj_replaceVertex_iff_of_ne_right, TripartiteFromTriangles.Graph.in₀₂_iff', Iso.map_adj_iff, Matrix.IsAdjMatrix.toGraph_adj, Walk.adj_of_infix_support, Walk.adj_penultimate, IsTuranMaximal.not_adj_iff_part_eq, adj_replaceVertex_iff_of_ne, mem_incidenceSet, boxProd_adj_right, lapMatrix_toLinearMap₂', map_singletonSubgraph, isVertexCover_preimage_iso, TopEdgeLabeling.labelGraph_adj, sInf_adj, two_mul_card_edgeFinset, Walk.map_copy, mem_support, adjMatrix_apply, homOfConnectedComponents_apply, adj_iff_exists_edge_coe, Coloring.mem_colorClass, exists_bijective_of_forall_ncard_le, Path.mapEmbedding_coe, dotProduct_mulVec_adjMatrix, Subgraph.IsInduced.adj, sum_adj, IsNClique.exists_not_adj_of_cliqueFree_succ, Iso.connectedComponentEquiv_symm_apply, Embedding.apply_mem_neighborSet_iff, adj_injective, Iso.reachable_iff, regularityReduced_adj, Embedding.sumInr_apply, Subgraph.spanningHom_injective, Copy.topEmbedding_apply, card_le_chromaticNumber_iff_forall_surjective, TripartiteFromTriangles.Graph.in₀₁_iff', Iso.sumComm_apply, TripartiteFromTriangles.Graph.in₂₁_iff', card_edgeFinset_map, adj_replaceVertex_iff_of_ne_left, Iso.sumBoxProdDistrib_apply, Iso.symm_apply_reachable, pathGraph_adj, Preconnected.exists_adj_of_nontrivial, cycleGraph_adj', Subgraph.comap_verts, hasseDualIso_apply, Embedding.map_adj_iff, induceUnivIso_apply, Iso.map_symm_apply, Copy.toHom_apply, completeMultipartiteGraph.topEmbedding_apply_fst, toTopEdgeLabeling_get, Hom.coe_id, edgeFinset_map, TripartiteFromTriangles.Graph.in₁₀_iff, Embedding.sumInl_apply, Walk.exists_adj_adj_not_adj_ne, Embedding.mapNeighborSet_apply_coe, Walk.adj_of_length_eq_one, deleteIncidenceSet_adj, mem_commonNeighbors, eccent_le_one_iff, Embedding.map_mem_edgeSet_iff, Copy.injective, Subgraph.adj_sub, degree_pos_iff_exists_adj, Walk.map_mapToSubgraph_eq_induce, disjoint_edge, Walk.darts_map, Subgraph.coe_adj, adj_and_reachable_delete_edges_iff_exists_cycle, Walk.map_nil, boxProd_adj_left, isBipartiteWith_neighborFinset, isIndepSet_iff, Walk.map_map, IsTuranMaximal.equivalence_not_adj, Iso.map_mem_edgeSet_iff, isClique_pair, le_iff_adj, IsPathGraph3Compl.not_adj_fst, completeEquipartiteGraph_adj, boxProdComm_symm_apply, isBridge_iff_adj_and_forall_walk_mem_edges, Hom.mapEdgeSet_coe, sup_adj, Iso.apply_mem_neighborSet_iff, fromEdgeSet_adj, Hom.map_mem_edgeSet, Subgraph.iInf_adj, cliqueFinset_map_of_equiv, map_adj, IsPathGraph3Compl.not_adj_snd, Subgraph.sInf_adj, interedges_def, ConnectedComponent.adj_spanningCoe_toSimpleGraph, TripartiteFromTriangles.Graph.in₀₂_iff, boxProdAssoc_apply, adj_edge, top_adj, ConnectedComponent.iso_inv_image_comp_eq_iff_eq_map, compl_adj, mem_neighborSet, Hom.mapDart_apply, Walk.IsSubwalk.map, Subgraph.adj_iff_of_neighborSet_equiv, Subgraph.edgeSet_map, ne_bot_iff_exists_adj, map_adj_apply, eccent_eq_one_iff, incMatrix_mul_transpose, le_chromaticNumber_iff_forall_surjective, iInf_adj, Subgraph.map_verts, Coloring.not_adj_of_mem_colorClass, Subgraph.spanningCoeEquivCoeOfSpanning_apply_coe, Embedding.coe_comp, ConnectedComponent.toSimpleGraph_hom_apply, Hom.comap_apply, extremalNumber_of_fintypeCard_eq, cliqueFinset_map, completeBipartiteGraph_adj, symm, isVertexCover_image_iso, mk_mem_interedges_iff, Copy.injective', dist_eq_one_iff_adj, hasse_adj, unreduced_edges_subset, induceHomOfLE_apply, deleteEdges_adj, Walk.IsCycle.adj_toSubgraph_iff_of_isCycles, isBridge_iff, Hom.coe_comp, Subgraph.map_adj, comap_adj, isClique_insert_of_notMem, Walk.reverse_map, ConnectedComponent.iso_image_comp_eq_map_iff_eq_comp, colorable_iff_exists_bdd_nat_coloring, isBridge_iff_adj_and_forall_cycle_notMem, Iso.mapNeighborSet_apply_coe, sSup_adj, cycleGraph_adj, Iso.comap_apply, Walk.map_mapToSubgraph_eq_induce_id, ne_top_iff_exists_not_adj, is3Clique_iff, Path.mapEmbedding_injective, isBipartiteWith_bipartiteBelow, isClique_iff_isChain_adj, Walk.length_map, Walk.adj_getVert_succ, Subgraph.hom_injective, triangle_counting', TripartiteFromTriangles.Graph.in₁₂_iff', edge_adj, TripartiteFromTriangles.Graph.in₂₀_iff', Walk.chain'_adj_support, mem_interedges_iff, isBipartiteWith_neighborSet', Iso.connectedComponentEquiv_trans, mem_neighborFinset, Iso.boxProdSumDistrib_symm_apply, set_walk_length_succ_eq, sdiff_adj, Reachable.map, reachable_iff_reflTransGen, adj_of_mem_walk_support, Hom.mapNeighborSet_coe, isClique_iff, Iso.boxProdSumDistrib_apply, bot_adj, Subgraph.Adj.adj_sub, Iso.boxProdSumDistrib_toEquiv, ext_iff, eq_bot_iff_forall_not_adj, isClique_insert, Iso.degree_eq, turanGraph_adj, ConnectedComponent.map_mk, degree_eq_sum_if_adj, cycleGraph_one_adj, symm_adj, Subgraph.spanningCoeEquivCoeOfSpanning_symm_apply, loopless, mk'_mem_incidenceSet_left_iff, isBipartiteWith_neighborSet, isIndepSet_iff_isAntichain_adj, Embedding.map_apply, TripartiteFromTriangles.Graph.not_in₂₂, TripartiteFromTriangles.Graph.in₀₁_iff, between_adj, Coloring.color_classes_independent, adj_congr_of_sym2, disjoint_left, TripartiteFromTriangles.Graph.in₂₀_iff, boxProd_adj, iInf_adj_of_nonempty, boxProdAssoc_symm_apply, cliqueFreeOn_two, Subgraph.spanningHom_apply, Walk.adj_of_mem_edges, TripartiteFromTriangles.Graph.in₁₀_iff', completeMultipartiteGraph.topEmbedding_apply_snd, Iso.mapNeighborSet_symm_apply_coe, Walk.isChain_adj_support, mk'_apply_adj, Iso.sumAssoc_apply, Embedding.comap_apply, TripartiteFromTriangles.Graph.in₁₂_iff, Iso.sumBoxProdDistrib_symm_apply, FirstOrder.Language.simpleGraphOfStructure_adj, eq_top_iff_forall_ne_adj, irrefl, Walk.edgeSet_map, toSubgraph_adj, Subgraph.top_adj, not_isClique_iff, Coloring.surjOn_of_card_le_isClique, Embedding.coe_completeGraph, is3Clique_triple_iff, sInf_adj_of_nonempty, fromRel_adj, induceUnivIso_symm_apply_coe, Walk.map_append, ComponentCompl.exists_adj_boundary_pair, Subgraph.Adj.adj_sub', lineGraph_adj_iff_exists, ConnectedComponent.toSimpleGraph_adj, neighborFinset_eq_filter, reachable_or_compl_adj, Walk.map_eq_of_eq, Embedding.mapEdgeSet_apply, Embedding.coe_toHom, Dart.adj, Subgraph.spanningCoe_adj, iSup_adj, Coloring.odd_length_iff_not_congr, circulantGraph_adj_translate, Subgraph.inclusion_apply_coe, hasseDualIso_symm_apply, Walk.support_map, boxProdRight_apply, isBridge_iff_adj_and_not_isEdgeConnected_two, cycleGraph_zero_adj, chromaticNumber_eq_iff_forall_surjective, Iso.mapEdgeSet_apply, mk'_mem_incidenceSet_iff, Walk.edges_map, induce_adj, Reachable.coe_subgraphMap, Subgraph.Adj.coe, adj_le_reachable, Iso.connectedComponentEquiv_apply, Subgraph.hom_apply, Coloring.mem_colorClasses, adj_inj, Iso.coe_comp, Hom.injective_of_top_hom, mem_edgeSet, isBipartiteWith_bipartiteAbove, reachable_eq_reflTransGen, Hom.coe_ofLE, Walk.adj_snd, edge_le_iff, Partition.independent, not_adj_replaceVertex_same, adj_iff_exists_edge, adj_of_mem_incidenceSet, circulantGraph_adj, Walk.map_eq_nil_iff, EdgeLabeling.labelGraph_adj, TripartiteFromTriangles.Graph.not_in₀₀, Walk.exists_length_eq_one_iff, edist_eq_one_iff_adj, Subgraph.inclusion.injective, Iso.sumAssoc_symm_apply, mk'_mem_incidenceSet_right_iff, Coloring.even_length_iff_congr, TripartiteFromTriangles.Graph.not_in₁₁, Walk.getVert_map, TripartiteFromTriangles.Graph.in₂₁_iff, isBipartiteWith_neighborFinset', Iso.sumBoxProdDistrib_toEquiv, chromaticNumber_eq_card_iff_forall_surjective, Iso.mapEdgeSet_symm_apply, deleteUniversalVerts_adj, boxProdLeft_apply, IsPathGraph3Compl.adj, degree_eq_one_iff_existsUnique_adj, Iso.map_apply, adj_comm, boxProdComm_apply, Iso.comap_symm_apply, Walk.toSubgraph_map, Iso.sumComm_symm_apply, Subgraph.coe_hom, Subgraph.comap_adj, inf_adj, edist_le_one_iff_adj_or_eq, Hom.apply_mem_neighborSet, Copy.coe_toHom, Hom.ofLE_apply

SimpleGraph.Subgraph

Definitions

NameCategoryTheorems
Adj 📖MathDef
47 mathmath: degree_eq_one_iff_unique_adj, sup_adj, isPerfectMatching_iff, SimpleGraph.subgraphOfAdj_adj, SimpleGraph.Walk.toSubgraph_adj_iff, IsInduced.adj, induce_adj, mem_edgeSet, SimpleGraph.singletonSubgraph_adj, inf_adj, SimpleGraph.Walk.toSubgraph_adj_penultimate, spanningCoe_inj, coe_adj, SimpleGraph.Walk.adj_toSubgraph_mapLe, SimpleGraph.ConnectedComponent.odd_matches_node_outside, sSup_adj, iInf_adj, sInf_adj, adj_comm, adj_iff_of_neighborSet_equiv, symm, degree_eq_one_iff_existsUnique_adj, adj_congr_of_sym2, SimpleGraph.Walk.IsCycle.adj_toSubgraph_iff_of_isCycles, deleteEdges_adj, map_adj, not_bot_adj, mem_neighborSet, SimpleGraph.Walk.toSubgraph_adj_snd, sInf_adj_of_nonempty, SimpleGraph.Walk.adj_toSubgraph_iff_mem_edges, SimpleGraph.toSubgraph_adj, top_adj, iSup_adj, deleteVerts_adj, iInf_adj_of_nonempty, spanningCoe_adj, coeSubgraph_adj, ext_iff, degree_pos_iff_exists_adj, SimpleGraph.Walk.toSubgraph_adj_getVert, Preconnected.exists_adj_of_nontrivial, mem_support, loopless, SimpleGraph.deleteUniversalVerts_adj, comap_adj, restrict_adj

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