Theorems · Theorem · category theory

CategoryTheory.Iso.inv_hom_id_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (self : X ≅ Y) {Z : C} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp self.inv (CategoryTheory.CategoryStruct.comp self.hom h) = h

Composition of the two directions of an isomorphism in reverse order is the identity on the target.

Defined in

Mathlib.CategoryTheory.Iso

Cited by

275 results in Mathlib

Foundations

Depth 6 from the axioms, rests on 17 definitions · uses Quot.sound

Assumes

CategoryTheory.Category