Theorems · Definition · category theory

CategoryTheory.Functor.isPointwiseLeftKanExtensionLeftKanExtensionUnit

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        (L : CategoryTheory.Functor C D) →
          {H : Type u_3} →
            [inst_2 : CategoryTheory.Category.{v_3, u_3} H] →
              (F : CategoryTheory.Functor C H) →
                [inst_3 : L.HasPointwiseLeftKanExtension F] →
                  (CategoryTheory.Functor.LeftExtension.mk (L.leftKanExtension F)
                      (L.leftKanExtensionUnit F)).IsPointwiseLeftKanExtension

If there exists a pointwise left Kan extension of F along L, then L.lan.obj G is a pointwise left Kan extension of F.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Adjunction

Cited by

7 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.HasPointwiseLeftKanExtension