Theorems · Theorem · category theory

CategoryTheory.Adjunction.homEquiv_counit

∀ {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) (X : C) (Y : D) (g : X ⟶ G.obj Y),
  (adj.homEquiv X Y).symm g = CategoryTheory.CategoryStruct.comp (F.map g) (adj.counit.app Y)

Alias of CategoryTheory.Adjunction.homEquiv_symm_apply.

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

30 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category