Theorems · Definition · category theory

CategoryTheory.Adjunction.CoreHomEquiv.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} →
            CategoryTheory.Adjunction.CoreHomEquiv F G → (X : C) → (Y : D) → (F.obj X ⟶ Y) ≃ (X ⟶ G.obj Y)

The equivalence between Hom (F X) Y and Hom X (G Y)

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

8 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category