Theorems · Theorem · category theory

CategoryTheory.Equivalence.unit_inverse_comp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (e : C ≌ D) (Y : D),
  CategoryTheory.CategoryStruct.comp (e.unit.app (e.inverse.obj Y)) (e.inverse.map (e.counit.app Y)) =
    CategoryTheory.CategoryStruct.id (e.inverse.obj Y)

The other triangle equality. The proof follows the following proof in Globular: http://globular.science/1905.001

Defined in

Mathlib.CategoryTheory.Equivalence

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category