preservesBiproductsOfShape_of_preservesProductsOfShape

English

If a functor preserves biproducts for shape J, it preserves biproducts of shape J (tautology in type classes).

Русский

Если функтор сохраняет биопродукты формы J, он сохраняет биопродукты формы J (тождейно в классах типов).

LaTeX

$$$[PreservesBiproductsOfShape J F] \Rightarrow \mathrm{PreservesBiproductsOfShape} J F$$$

Lean4

/-- A functor between preadditive categories that preserves (zero morphisms and) finite products
preserves finite biproducts. -/
theorem preservesBiproductsOfShape_of_preservesProductsOfShape [PreservesLimitsOfShape (Discrete J) F] :
    PreservesBiproductsOfShape J F where preserves {_} := preservesBiproduct_of_preservesProduct F

Похожие утверждения