of_hasFiniteProducts — Mathlib

English

In a preadditive category, finite coproducts imply finite biproducts.

Русский

В преддобавительной категории конечные coproducts приводят к конечным билипроизводным.

LaTeX

$$HasFiniteCoproducts C ⇒ HasFiniteBiproducts C$$

Lean4

/-- A preadditive category with finite products has finite biproducts. -/
theorem of_hasFiniteProducts [HasFiniteProducts C] : HasFiniteBiproducts C :=
  ⟨fun _ => { has_biproduct := fun _ => HasBiproduct.of_hasProduct _ }⟩

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