Theorems · Definition · category theory

CategoryTheory.Limits.coprod.mapIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {W X Y Z : C} →
      [inst_1 : CategoryTheory.Limits.HasBinaryCoproduct W X] →
        [inst_2 : CategoryTheory.Limits.HasBinaryCoproduct Y Z] → (W ≅ Y) → (X ≅ Z) → (W ⨿ X ≅ Y ⨿ Z)

If the coproducts W ⨿ X and Y ⨿ Z exist, then every pair of isomorphisms f : W ≅ Y and g : W ≅ Z induces an isomorphism coprod.mapIso f g : W ⨿ X ≅ Y ⨿ Z.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts

Cited by

4 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryCoproductCategoryTheory.Limits.HasBinaryCoproduct