instHasExactLimitsOfShapeOfHasFiniteColimitsOfPreservesFiniteColimitsFunctorOppositeSheafToPresheaf

English

ShrinkHoms construction preserves Grothendieck abelian property: if C is Grothendieck abelian, then ShrinkHoms(C) is Grothendieck abelian.

Русский

Конструкция ShrinkHoms сохраняет свойство Гротениджа абелевой категории: если C — Гротениджевая абелева, то ShrinkHoms(C) тоже такова.

LaTeX

$$$\mathrm{IsGrothendieckAbelian}(\mathrm{ShrinkHoms}(C))$$$

Lean4

instance [HasFiniteColimits A] [HasLimitsOfShape K A] [HasExactLimitsOfShape K A]
    [PreservesFiniteColimits (sheafToPresheaf J A)] : HasExactLimitsOfShape K (Sheaf J A) :=
  HasExactLimitsOfShape.domain_of_functor K (sheafToPresheaf J A)

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