Theorems · Theorem · category theory

CategoryTheory.Functor.fun_inv_map

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) [inst_2 : F.IsEquivalence] (X Y : D) (f : X ⟶ Y),
  F.map (F.inv.map f) =
    CategoryTheory.CategoryStruct.comp (F.asEquivalence.counit.app X)
      (CategoryTheory.CategoryStruct.comp f (F.asEquivalence.counitInv.app Y))

Defined in

Mathlib.CategoryTheory.Equivalence

Cited by

1 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsEquivalence