Theorems · Definition · category theory

CategoryTheory.Functor.Final.isColimitWhiskerEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) →
          [F.Final] →
            {E : Type u₃} →
              [inst_3 : CategoryTheory.Category.{v₃, u₃} E] →
                {G : CategoryTheory.Functor D E} →
                  (t : CategoryTheory.Limits.Cocone G) →
                    CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.Cocone.whisker F t) ≃
                      CategoryTheory.Limits.IsColimit t

When F : C ⥤ D is final, and t : Cocone G for some G : D ⥤ E, t.whisker F is a colimit cocone exactly when t is.

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

8 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FinalCategoryTheory.Category