Theorems · Theorem · category theory

CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac

∀ {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.PreservesPointwiseLeftKanExtension F L]
  [inst_5 : L.HasPointwiseLeftKanExtension F],
  CategoryTheory.CategoryStruct.comp (L.pointwiseLeftKanExtensionUnit (F.comp G))
      (L.whiskerLeft (G.pointwiseLeftKanExtensionCompIsoOfPreserves F L).inv) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.whiskerRight (L.pointwiseLeftKanExtensionUnit F) G)
      (L.associator (L.pointwiseLeftKanExtension F) G).hom

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Preserves

Cited by

2 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.PreservesPointwiseLeftKanExtensionCategoryTheory.Functor.HasPointwiseLeftKanExtension