preservesBinaryProducts_of_preservesKernels

English

If a functor preserves kernels, it preserves binary products; equivalently, preserves limits of shape Discrete WalkingPair.

Русский

Если деФФектор сохраняет ядра, он сохраняет двоичные продукты; эквивалентно сохранению пределов формы Discrete WalkingPair.

LaTeX

$$$PreservesLimitsOfShape(Discrete\ WalkingPair)\ F$ under kernel-preservation$$

Lean4

/-- A kernel-preserving functor between preadditive categories preserves binary products. -/
theorem preservesBinaryProducts_of_preservesKernels [∀ {X Y} (f : X ⟶ Y), PreservesLimit (parallelPair f 0) F] :
    PreservesLimitsOfShape (Discrete WalkingPair) F where
  preservesLimit := preservesLimit_of_iso_diagram F (diagramIsoPair _).symm

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