Theorems · Theorem · category theory
CategoryTheory.Functor.map_hom_inv_assoc
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) {X Y : C} (f : X ⟶ Y) [inst_2 : CategoryTheory.IsIso f] {Z : D} (h : F.obj X ⟶ Z),
CategoryTheory.CategoryStruct.comp (F.map f) (CategoryTheory.CategoryStruct.comp (F.map (CategoryTheory.inv f)) h) = h- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement and proof · cited by 467
- CategoryTheory.Functor.map_hom_invproof · cited by 2
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