of_hasFiniteCoproducts — Mathlib

English

If a category has finite coproducts, it has finite biproducts.

Русский

Если у категории есть конечные coproducts, то есть конечные билипроизводные.

LaTeX

$$HasFiniteCoproducts C ⇒ HasFiniteBiproducts C$$

Lean4

/-- A preadditive category with finite coproducts has finite biproducts. -/
theorem of_hasFiniteCoproducts [HasFiniteCoproducts C] : HasFiniteBiproducts C :=
  ⟨fun _ => { has_biproduct := fun _ => HasBiproduct.of_hasCoproduct _ }⟩

Похожие утверждения