Theorems · Theorem · category theory

CategoryTheory.Functor.ranCounit_app_app_ranAdjunction_unit_app_app

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (L : CategoryTheory.Functor C D) {H : Type u_3}
  [inst_2 : CategoryTheory.Category.{v_3, u_3} H]
  [inst_3 : ∀ (F : CategoryTheory.Functor C H), L.HasRightKanExtension F] (G : CategoryTheory.Functor D H) (X : C),
  CategoryTheory.CategoryStruct.comp (((L.ranAdjunction H).unit.app G).app (L.obj X))
      ((L.ranCounit.app (L.comp G)).app X) =
    CategoryTheory.CategoryStruct.id (((CategoryTheory.Functor.id (CategoryTheory.Functor D H)).obj G).obj (L.obj X))

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Adjunction

Cited by

1 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.HasRightKanExtension