Theorems · Theorem · category theory

CategoryTheory.IsIso.out

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {X Y : C} {f : X ⟶ Y} [self : CategoryTheory.IsIso f],
  ∃ inv,
    CategoryTheory.CategoryStruct.comp f inv = CategoryTheory.CategoryStruct.id X ∧
      CategoryTheory.CategoryStruct.comp inv f = CategoryTheory.CategoryStruct.id Y

The existence of an inverse morphism.

Defined in

Mathlib.CategoryTheory.Iso

Cited by

2 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.IsIso