Theorems · Theorem · category theory

CategoryTheory.Equivalence.fun_inv_map_assoc

∀ {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) {Z : D} (h : e.functor.obj (e.inverse.obj Y) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (e.functor.map (e.inverse.map f)) h =
    CategoryTheory.CategoryStruct.comp (e.counit.app X)
      (CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp (e.counitInv.app Y) h))

Defined in

Mathlib.CategoryTheory.Equivalence

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category