Theorems · Theorem · category theory
CategoryTheory.Iso.homCongr_apply
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y X₁ Y₁ : C} (α : X ≅ X₁) (β : Y ≅ Y₁) (f : X ⟶ Y),
(α.homCongr β) f = CategoryTheory.CategoryStruct.comp α.inv (CategoryTheory.CategoryStruct.comp f β.hom)- Defined in
- Mathlib.CategoryTheory.HomCongr
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- Equivstatement · cited by 8,337
- CategoryTheory.Iso.homstatement · cited by 7,684
- CategoryTheory.Iso.invstatement · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Iso.homCongrstatement and proof · cited by 30
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.LocalizerMorphism.homMap_compproof · cited by 2
- CategoryTheory.LocalizerMorphism.homMap_mapproof · cited by 2
- HomotopicalAlgebra.bijective_rightHomotopyClassToHomproof · cited by 2
- CategoryTheory.Iso.homCongr_transproof · cited by 1
- CategoryTheory.Functor.map_homCongrproof · cited by 1
- CategoryTheory.Iso.homCongr_reflproof · cited by 0
- CategoryTheory.Iso.homCongr_compproof · cited by 0