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arxiv: 1211.5294 · v4 · pith:NNCHQ4BWnew · submitted 2012-11-22 · 🧮 math.CT · math.AG

Gluing restricted nerves of infty-categories

Yifeng Liu , Weizhe Zheng This is my paper
classification 🧮 math.CT math.AG
keywords gluingcategoriescohomologyconstructequivalencesetaleinftyresults
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In this article, we develop a general technique for gluing subcategories of $\infty$-categories. We obtain categorical equivalences between simplicial sets associated to certain multisimplicial sets. Such equivalences can be used to construct functors in different contexts. One of our results generalizes Deligne's gluing theory developed in the construction of the extraordinary pushforward operation in \'etale cohomology of schemes. Our results are applied in subsequent articles to construct Grothendieck's six operations in \'etale cohomology of Artin stacks.

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  1. A characterization of sheaves among six functor formalisms on $\mathrm{LCH}$

    math.AT 2026-06 unverdicted novelty 7.0

    Sheaf categories are the unique six functor formalisms on LCH spaces satisfying natural properties, implying equivalence for continuous formalisms.