Theorems · Definition · category theory

CategoryTheory.Functor.Final.colimitIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) →
          [inst_2 : F.Final] →
            {E : Type u₃} →
              [inst_3 : CategoryTheory.Category.{v₃, u₃} E] →
                (G : CategoryTheory.Functor D E) →
                  [inst_4 : CategoryTheory.Limits.HasColimit G] →
                    CategoryTheory.Limits.colimit (F.comp G) ≅ CategoryTheory.Limits.colimit G

When F : C ⥤ D is final, and G : D ⥤ E has a colimit, then F ⋙ G has a colimit also and colimit (F ⋙ G) ≅ colimit G.

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

8 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FinalCategoryTheory.CategoryCategoryTheory.Limits.HasColimit