Theorems · Theorem · category theory

CategoryTheory.Adjunction.homEquiv_ofNatIsoLeft_apply

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F G : CategoryTheory.Functor C D} {H : CategoryTheory.Functor D C} (adj : F ⊣ H) (iso : F ≅ G) {X : C} {Y : D}
  (f : G.obj X ⟶ Y),
  ((adj.ofNatIsoLeft iso).homEquiv X Y) f = (adj.homEquiv X Y) (CategoryTheory.CategoryStruct.comp (iso.hom.app X) f)

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category