Theorems · Definition · category theory

CategoryTheory.Functor.asEquivalence

{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] → C ≌ D

Interpret a functor that is an equivalence as an equivalence.

Defined in

Mathlib.CategoryTheory.Equivalence

Cited by

58 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsEquivalence