Theorems · Theorem · category theory

CategoryTheory.Adjunction.toEquivalence_unitIso_hom_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (adj : F ⊣ G)
  [inst_2 : ∀ (X : C), CategoryTheory.IsIso (adj.unit.app X)]
  [inst_3 : ∀ (Y : D), CategoryTheory.IsIso (adj.counit.app Y)] (X : C),
  adj.toEquivalence.unitIso.hom.app X = adj.unit.app X

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIsoCategoryTheory.IsIso