Theorems · Theorem · category theory

CategoryTheory.Iso.inv_hom_id

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

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

Defined in

Mathlib.CategoryTheory.Iso

Cited by

308 results in Mathlib

Foundations

Depth 3 from the axioms, rests on 12 definitions · uses no axioms

Assumes

CategoryTheory.Category