Theorems · Definition · category theory

CategoryTheory.Adjunction.homEquiv

{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} → (F ⊣ G) → (X : C) → (Y : D) → (F.obj X ⟶ Y) ≃ (X ⟶ G.obj Y)

The hom set equivalence associated to an adjunction.

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

202 results in Mathlib

Foundations

Depth 23 from the axioms, rests on 116 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category