preservesBinaryBiproducts_of_preservesBinaryProducts

English

If F preserves the binary biproducts, then F preserves biproducts of any pair X,Y; equivalently, F preserves limits of shape Discrete WalkingPair.

Русский

Если F сохраняет бинарные би-производные, то он сохраняет би-производные любой пары X,Y; эквивалентно: F сохраняет пределы формы Discrete WalkingPair.

LaTeX

$$$$\\PreservesBinaryBiproducts F\\;\\Rightarrow\\; \\PreservesLimitsOfShape(\\mathrm{Discrete WalkingPair}) F.$$$$

Lean4

/-- A functor between preadditive categories that preserves (zero morphisms and) binary products
preserves binary biproducts. -/
theorem preservesBinaryBiproducts_of_preservesBinaryProducts [PreservesLimitsOfShape (Discrete WalkingPair) F] :
    PreservesBinaryBiproducts F where preserves {_} {_} := preservesBinaryBiproduct_of_preservesBinaryProduct F

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