Theorems · Theorem · category theory

CategoryTheory.Equivalence.fun_inv_map

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (e : C ≌ D) (X Y : D) (f : X ⟶ Y),
  e.functor.map (e.inverse.map f) =
    CategoryTheory.CategoryStruct.comp (e.counit.app X) (CategoryTheory.CategoryStruct.comp f (e.counitInv.app Y))

Defined in

Mathlib.CategoryTheory.Equivalence

Cited by

9 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category