Theorems · Theorem · category theory

CategoryTheory.Adjunction.right_triangle_components_assoc

∀ {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} (self : F ⊣ G) (Y : D) {Z : C} (h : G.obj Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (self.unit.app (G.obj Y))
      (CategoryTheory.CategoryStruct.comp (G.map (self.counit.app Y)) h) =
    h

Equality of the composition of the unit and counit with the identity G ⟶ GFG ⟶ G = 𝟙

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

9 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category