preservesBinaryBiproducts_of_preservesBinaryCoproducts

English

If F preserves (zero morphisms and) binary biproducts, then F preserves binary biproducts in the target, i.e. preserves biproducts of images equals image of biproducts.

Русский

Если F сохраняет (нуль-морфизмы и) бинарные би-производные, то F сохраняет би-производные изображений, то есть сохраняет би-производные образов.

LaTeX

$$$$\\PreservesBinaryBiproducts F.$$$$

Lean4

/-- A functor between preadditive categories that preserves (zero morphisms and) binary coproducts
preserves binary biproducts. -/
theorem preservesBinaryBiproducts_of_preservesBinaryCoproducts [PreservesColimitsOfShape (Discrete WalkingPair) F] :
    PreservesBinaryBiproducts F where preserves {_} {_} := preservesBinaryBiproduct_of_preservesBinaryCoproduct F

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