Theorems · Definition · category theory

CategoryTheory.Functor.HasPointwiseLeftKanExtensionAt

{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] →
            CategoryTheory.Functor C D → CategoryTheory.Functor C H → D → Prop

The condition that a functor F has a pointwise left Kan extension along L at Y. It means that the functor CostructuredArrow.proj L Y ⋙ F : CostructuredArrow L Y ⥤ H has a colimit.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Pointwise

Cited by

13 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category