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Segal Sheafification and Refinement-Invariant Descent
2025-11-08
We establish categorical results on the interaction between Segal conditions and
hypersheafification in derived moduli problems.
First, we show that $\tau$-hypersheafification, viewed as a left exact reflector,
preserves Segal objects and hence extends Segal presentations of moduli functors to
stacks.
Second, we prove a refinement-invariant descent theorem: hypercovers refined by
Segal morphisms yield equivalent descent data, ensuring stability under
local refinements.
As an application, we deduce compatibility of mapping stacks and moduli of
perfect complexes with Segal sheafification.
These results situate Segal-type models within the general framework of descent
theory in $\infty$-categories, with further consequences for arithmetic and
Tannakian moduli.
Ссылка для цитирования:
Kundnani R. T., Kant Sh., Alam K. 2025. Segal Sheafification and Refinement-Invariant Descent. PREPRINTS.RU. https://doi.org/10.24108/preprints-3113871
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