Theorems · Definition · category theory

CategoryTheory.Limits.isColimitCoconeOfFiberwiseCocone

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {F : CategoryTheory.Functor C CategoryTheory.Cat} →
      {H : Type u₂} →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} H] →
          {G : CategoryTheory.Functor (CategoryTheory.Grothendieck F) H} →
            [inst_2 :
                ∀ {X Y : C} (f : X ⟶ Y),
                  CategoryTheory.Limits.HasColimit
                    ((F.map f).toFunctor.comp ((CategoryTheory.Grothendieck.ι F Y).comp G))] →
              {c : CategoryTheory.Limits.Cocone (CategoryTheory.Limits.fiberwiseColimit G)} →
                CategoryTheory.Limits.IsColimit c →
                  CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit c)

If a cocone c over a functor G : Grothendieck F ⥤ H is a colimit, then the induced cocone coconeOfFiberwiseCocone G c

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Grothendieck

Cited by

1 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimit