preservesBinaryCoproducts_of_preservesCokernels

English

A functor preserving cokernels preserves binary coproducts (cokernels determine coproducts in preadditive settings).

Русский

Функтор, сохраняющий cokernels, сохраняет двоичные coproducts.

LaTeX

$$$PreservesCoproducts_of_preservesCokernels F$$$

Lean4

/-- A cokernel-preserving functor between preadditive categories preserves binary coproducts. -/
theorem preservesBinaryCoproducts_of_preservesCokernels [∀ {X Y} (f : X ⟶ Y), PreservesColimit (parallelPair f 0) F] :
    PreservesColimitsOfShape (Discrete WalkingPair) F where
  preservesColimit := preservesColimit_of_iso_diagram F (diagramIsoPair _).symm

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