Theorems · Definition · category theory

CategoryTheory.SemiadditiveOfBinaryBiproducts.addCommMonoidHomOfHasBinaryBiproducts

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      [CategoryTheory.Limits.HasBinaryBiproducts C] → (X Y : C) → AddCommMonoid (X ⟶ Y)

In a category with binary biproducts, the morphisms form a commutative monoid.

Defined in: Mathlib.CategoryTheory.Preadditive.OfBiproducts
Cited by: 4 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproducts

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Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
AddCommMonoidstatement · cited by 12,281
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_left_additionstatement · cited by 1
CategoryTheory.SemiadditiveOfBinaryBiproducts.add_compstatement · cited by 0
CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_right_additionstatement · cited by 0
CategoryTheory.SemiadditiveOfBinaryBiproducts.comp_addstatement · cited by 0