instPreservesFiniteProductsFunctorColimOfPreadditive

English

If A is a preadditive category, then the colimit functor over shape J preserves finite products.

Русский

Если A — прeадитивная категория, то колиматорная функция сохраняет конечно-логарифмические произведения.

LaTeX

$$$\mathrm{PreservesFiniteProducts}(\mathrm{colim}_{J}(C))$$$

Lean4

instance [Preadditive A] : PreservesFiniteProducts (colim (J := J) (C := A)) where
  preserves
    _ := by
    apply (config := { allowSynthFailures := true }) preservesProductsOfShape_of_preservesBiproductsOfShape
    apply preservesBiproductsOfShape_of_preservesCoproductsOfShape

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