Theorems · Theorem · category theory

CategoryTheory.Functor.pointwiseLeftKanExtension_desc_app

∀ {C : Type u_1} {D : Type u_2} {H : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Category.{v_4, u_4} H]
  (L : CategoryTheory.Functor C D) (F : CategoryTheory.Functor C H) [inst_3 : L.HasPointwiseLeftKanExtension F]
  (G : CategoryTheory.Functor D H) (α : F ⟶ L.comp G) (Y : D),
  ((L.pointwiseLeftKanExtension F).descOfIsLeftKanExtension (L.pointwiseLeftKanExtensionUnit F) G α).app Y =
    CategoryTheory.Limits.colimit.desc ((CategoryTheory.CostructuredArrow.proj L Y).comp F)
      (L.costructuredArrowMapCocone F G α Y)

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Pointwise

Cited by

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.HasPointwiseLeftKanExtension