Theorems · Definition · category theory

CategoryTheory.Functor.inv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) → [F.IsEquivalence] → CategoryTheory.Functor D C

A quasi-inverse D ⥤ C to a functor that F : C ⥤ D that is an equivalence, i.e. faithful, full, and essentially surjective.

Defined in

Mathlib.CategoryTheory.Equivalence

Cited by

27 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsEquivalence