Theorems · Definition · category theory

CategoryTheory.Limits.coproductIsCoproduct

{β : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      (f : β → C) →
        [inst_1 : CategoryTheory.Limits.HasCoproduct f] →
          CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.Cofan.mk (∐ f) (CategoryTheory.Limits.Sigma.ι f))

The cofan constructed of the inclusions from the coproduct is colimiting.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Products

Cited by

31 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoproduct