Theorems · Definition · category theory

CategoryTheory.preservesColimitIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          {J : Type w} →
            [inst_2 : CategoryTheory.Category.{w', w} J] →
              (F : CategoryTheory.Functor J C) →
                [inst_3 : CategoryTheory.Limits.PreservesColimit F G] →
                  [inst_4 : CategoryTheory.Limits.HasColimit F] →
                    G.obj (CategoryTheory.Limits.colimit F) ≅ CategoryTheory.Limits.colimit (F.comp G)

If G preserves colimits, we have an isomorphism from the image of the colimit of a functor F to the colimit of the functor F ⋙ G.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Limits

Cited by

17 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesColimitCategoryTheory.Limits.HasColimit