Theorems · Theorem · category theory

CategoryTheory.Adjunction.left_triangle_components

∀ {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) (X : C),
  CategoryTheory.CategoryStruct.comp (F.map (self.unit.app X)) (self.counit.app (F.obj X)) =
    CategoryTheory.CategoryStruct.id (F.obj X)

Equality of the composition of the unit and counit with the identity F ⟶ FGF ⟶ F = 𝟙

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

25 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category