Theorems · Definition · category theory

CategoryTheory.Limits.Sigma.isoColimit

{α : Type w₂} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      (X : CategoryTheory.Functor (CategoryTheory.Discrete α) C) →
        [inst_1 : CategoryTheory.Limits.HasCoproduct fun j => X.obj { as := j }] →
          [inst_2 : CategoryTheory.Limits.HasColimit X] →
            (∐ fun j => X.obj { as := j }) ≅ CategoryTheory.Limits.colimit X

The isomorphism ∐ (fun j => X.obj (Discrete.mk j)) ≅ colimit X.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Products

Cited by

7 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductCategoryTheory.Limits.HasColimit