Theorems · Theorem · category theory

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

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category