Theorems · Theorem · category theory

CategoryTheory.Functor.isEquivalence_of_comp_right

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u_1} [inst_2 : CategoryTheory.Category.{v_1, u_1} E] (F : CategoryTheory.Functor C D)
  (G : CategoryTheory.Functor D E) [G.IsEquivalence] [(F.comp G).IsEquivalence], F.IsEquivalence

If G and F ⋙ G are equivalence of categories, then F is also an equivalence.

Defined in

Mathlib.CategoryTheory.Equivalence

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsEquivalenceCategoryTheory.Functor.IsEquivalence