Theorems · Definition · category theory

CategoryTheory.Limits.PreservesColimitPair.iso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          (X Y : C) →
            [inst_2 : CategoryTheory.Limits.HasBinaryCoproduct X Y] →
              [inst_3 : CategoryTheory.Limits.HasBinaryCoproduct (G.obj X) (G.obj Y)] →
                [CategoryTheory.Limits.PreservesColimit (CategoryTheory.Limits.pair X Y) G] →
                  G.obj X ⨿ G.obj Y ≅ G.obj (X ⨿ Y)

If G preserves the coproduct of (X,Y), then the coproduct comparison map for G at (X,Y) is an isomorphism.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts

Cited by

4 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasBinaryCoproductCategoryTheory.Limits.HasBinaryCoproductCategoryTheory.Limits.PreservesColimit