Theorems · Theorem · category theory

CategoryTheory.Adjunction.homEquiv_naturality_right_symm

∀ {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 Y' : D} (f : X ⟶ G.obj Y)
  (g : Y ⟶ Y'),
  (adj.homEquiv X Y').symm (CategoryTheory.CategoryStruct.comp f (G.map g)) =
    CategoryTheory.CategoryStruct.comp ((adj.homEquiv X Y).symm f) g

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

8 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category