Theorems · Theorem · category theory

CategoryTheory.Functor.PreservesRightKanExtension.mk_of_preserves_isUniversal

∀ {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) (E : L.RightExtension F) (hE : CategoryTheory.CostructuredArrow.IsUniversal E),
  Nonempty
      (CategoryTheory.CostructuredArrow.IsUniversal
        ((CategoryTheory.Functor.RightExtension.postcompose₂ L F G).obj E)) →
    G.PreservesRightKanExtension F L

Show that G preserves right Kan extensions if it maps some right Kan extension to a left Kan extension, phrased in terms of IsUniversal.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Preserves

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category