Theorems · Theorem · category theory

CategoryTheory.Limits.coprod.map_swap

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A B X Y : C} (f : A ⟶ B) (g : X ⟶ Y)
  [inst_1 : CategoryTheory.Limits.HasColimitsOfShape (CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair) C],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coprod.map (CategoryTheory.CategoryStruct.id X) f)
      (CategoryTheory.Limits.coprod.map g (CategoryTheory.CategoryStruct.id B)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coprod.map g (CategoryTheory.CategoryStruct.id A))
      (CategoryTheory.Limits.coprod.map (CategoryTheory.CategoryStruct.id Y) f)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShape