Theorems · Definition · category theory

CategoryTheory.Functor.isLimitConeOfIsRightKanExtension

{C : Type u_1} →
  {H : Type u_3} →
    {D : Type u_4} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_3, u_3} H] →
          [inst_2 : CategoryTheory.Category.{v_4, u_4} D] →
            (F' : CategoryTheory.Functor D H) →
              {L : CategoryTheory.Functor C D} →
                {F : CategoryTheory.Functor C H} →
                  (α : L.comp F' ⟶ F) →
                    [inst_3 : F'.IsRightKanExtension α] →
                      {c : CategoryTheory.Limits.Cone F} →
                        CategoryTheory.Limits.IsLimit c →
                          CategoryTheory.Limits.IsLimit (F'.coneOfIsRightKanExtension α c)

If c is a limit cone for a functor F : C ⥤ H and α : L ⋙ F' ⟶ F is the counit of any right Kan extension F' : D ⥤ H of F along L : C ⥤ D, then coneOfIsRightKanExtension α c is a limit cone, too.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsRightKanExtension