Theorems · Theorem · category theory

CategoryTheory.Adjunction.counit_naturality

∀ {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} (adj : G ⊣ F) {X Y : C} (f : Y ⟶ X),
  CategoryTheory.CategoryStruct.comp (G.map (F.map f)) (adj.counit.app X) =
    CategoryTheory.CategoryStruct.comp (adj.counit.app Y) f

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

30 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category