Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.map_eq

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {W X Y Z : C} {f : W ⟶ Y} {g : X ⟶ Z},
  CategoryTheory.Limits.biprod.map f g =
    CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.fst
        (CategoryTheory.CategoryStruct.comp f CategoryTheory.Limits.biprod.inl) +
      CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.snd
        (CategoryTheory.CategoryStruct.comp g CategoryTheory.Limits.biprod.inr)

Defined in

Mathlib.CategoryTheory.Preadditive.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts