Theorems · Definition · category theory

CategoryTheory.Limits.fiberwiseColimCompColimIso

{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] →
          [inst_2 : ∀ (c : C), CategoryTheory.Limits.HasColimitsOfShape (↑(F.obj c)) H] →
            [inst_3 : CategoryTheory.Limits.HasColimitsOfShape C H] →
              (CategoryTheory.Limits.fiberwiseColim F H).comp CategoryTheory.Limits.colim ≅ CategoryTheory.Limits.colim

The isomorphism colimitFiberwiseColimitIso induces an isomorphism of functors (J ⥤ C) ⥤ C between fiberwiseColim F H ⋙ colim and colim.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Grothendieck

Cited by

2 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasColimitsOfShape