Theorems · Theorem · category theory

CategoryTheory.Adjunction.CoreUnitCounit.right_triangle

∀ {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 : CategoryTheory.Adjunction.CoreUnitCounit F G),
  CategoryTheory.CategoryStruct.comp (G.whiskerLeft self.unit)
      (CategoryTheory.CategoryStruct.comp (G.associator F G).inv (CategoryTheory.Functor.whiskerRight self.counit G)) =
    CategoryTheory.NatTrans.id (G.comp (CategoryTheory.Functor.id C))

Equality of the composition of the unit, associator, and counit with the identity G ⟶ G (F G) ⟶ (F G) F ⟶ G = NatTrans.id G

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

0 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category