preservesBinaryBiproducts_of_preservesBiproducts

English

If a functor preserves a biproduct for the shape WalkingPair, it preserves binary biproducts.

Русский

Если функтор сохраняет би-производное для формы WalkingPair, он сохраняет бинарные би-производные.

LaTeX

$$$\text{PreservesBinaryBiproducts} F$ given $\text{PreservesBiproduct}(\text{pairFunction } X Y) F$$$

Lean4

/-- A functor that preserves biproducts of a pair preserves binary biproducts. -/
theorem preservesBinaryBiproducts_of_preservesBiproducts (F : C ⥤ D) [PreservesZeroMorphisms F]
    [PreservesBiproductsOfShape WalkingPair F] : PreservesBinaryBiproducts F where
  preserves {X} Y := preservesBinaryBiproduct_of_preservesBiproduct F X Y

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