Theorems · Theorem · category theory

CategoryTheory.Functor.PreservesRightKanExtension.mk_of_preserves_isRightKanExtension

∀ {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) (F' : CategoryTheory.Functor C B) (α : L.comp F' ⟶ F) [F'.IsRightKanExtension α],
  (F'.comp G).IsRightKanExtension
      (CategoryTheory.CategoryStruct.comp (L.associator F' G).inv (CategoryTheory.Functor.whiskerRight α G)) →
    G.PreservesRightKanExtension F L

Show that G preserves right Kan extensions if it maps some right Kan extension to a right Kan extension.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Preserves

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsRightKanExtension