Theorems · Definition · category theory

CategoryTheory.Functor.isPointwiseLeftKanExtensionOfIsLeftKanExtension

{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} →
                [L.HasPointwiseLeftKanExtension F] →
                  (F' : CategoryTheory.Functor D H) →
                    (α : F ⟶ L.comp F') →
                      [F'.IsLeftKanExtension α] →
                        (CategoryTheory.Functor.LeftExtension.mk F' α).IsPointwiseLeftKanExtension

If F admits a pointwise left Kan extension along L, then any left Kan extension of F along L is a pointwise left Kan extension.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Pointwise

Cited by

2 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.HasPointwiseLeftKanExtensionCategoryTheory.Functor.IsLeftKanExtension