Theorems · Theorem · category theory

CategoryTheory.Adjunction.adjunctionOfEquivRight_unit_app

∀ {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))
  (X : C),
  (CategoryTheory.Adjunction.adjunctionOfEquivRight e he).unit.app X =
    (e X (F.obj X)) (CategoryTheory.CategoryStruct.id (F.obj X))

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category