instPreservesFiniteColimitsSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreadditiveOfHasFiniteColimits

English

In a finitary extensive setting with finite colimits, the sheaf-to-presheaf functor preserves finite colimits.

Русский

В факторе с конечными колимитами сохраняется сопоставление шар и преприн.

LaTeX

$$$\mathrm{PreservesFiniteColimits}(\mathrm{sheafToPresheaf}(\mathrm{extensiveTopology}(C) , A))$$$

Lean4

instance [Preadditive A] [HasFiniteColimits A] : PreservesFiniteColimits (sheafToPresheaf (extensiveTopology C) A) where
  preservesFiniteColimits _ := inferInstance

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