Theorems · Definition · category theory

coprodIsoPushout

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasInitial C] →
      [inst_2 : CategoryTheory.Limits.HasPushouts C] →
        (X Y : C) →
          [inst_3 : CategoryTheory.Limits.HasBinaryCoproduct X Y] →
            X ⨿ Y ≅
              CategoryTheory.Limits.pushout (CategoryTheory.Limits.initial.to X) (CategoryTheory.Limits.initial.to Y)

In a category with an initial object and pushouts, a coproduct of objects X and Y is isomorphic to a pushout.

Defined in

Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts

Cited by

8 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasInitialCategoryTheory.Limits.HasPushoutsCategoryTheory.Limits.HasBinaryCoproduct