Theorems · Theorem · category theory

CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app

∀ {A : Type u_1} {B : Type u_2} {C : Type u_3} {D : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} A]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} B] [inst_2 : CategoryTheory.Category.{v_3, u_3} C]
  [inst_3 : CategoryTheory.Category.{v_4, u_4} D] (G : CategoryTheory.Functor B D) (F : CategoryTheory.Functor A B)
  (L : CategoryTheory.Functor A C) [inst_4 : G.PreservesRightKanExtension F L] [inst_5 : L.HasRightKanExtension F]
  (a : A),
  CategoryTheory.CategoryStruct.comp ((G.rightKanExtensionCompIsoOfPreserves F L).hom.app (L.obj a))
      ((L.rightKanExtensionCounit (F.comp G)).app a) =
    G.map ((L.rightKanExtensionCounit F).app a)

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Preserves

Cited by

1 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.PreservesRightKanExtensionCategoryTheory.Functor.HasRightKanExtension