Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.decomp_hom_from

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] {X Y : C}
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y] {Z : C} (f : X ⊞ Y ⟶ Z),
  ∃ f₁ f₂,
    f =
      CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.fst f₁ +
        CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.snd f₂

Defined in

Mathlib.CategoryTheory.Preadditive.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproduct