Theorems · Definition · category theory

CategoryTheory.Adjunction.adjunctionOfEquivRight

{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_obj : D → C} →
            (e : (X : C) → (Y : D) → (F.obj X ⟶ Y) ≃ (X ⟶ G_obj Y)) →
              (he :
                  ∀ (X' X : C) (Y : D) (f : X' ⟶ X) (g : F.obj X ⟶ Y),
                    (e X' Y) (CategoryTheory.CategoryStruct.comp (F.map f) g) =
                      CategoryTheory.CategoryStruct.comp f ((e X Y) g)) →
                F ⊣ CategoryTheory.Adjunction.rightAdjointOfEquiv e he

Show that the functor given by rightAdjointOfEquiv is indeed right adjoint to F. Dual to adjunctionOfEquivLeft.

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

5 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category