Gluing restricted nerves of $\infty$-categories
Category Theory
2015-06-09 v4 Algebraic Geometry
Abstract
In this article, we develop a general technique for gluing subcategories of -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.
Keywords
Cite
@article{arxiv.1211.5294,
title = {Gluing restricted nerves of $\infty$-categories},
author = {Yifeng Liu and Weizhe Zheng},
journal= {arXiv preprint arXiv:1211.5294},
year = {2015}
}
Comments
54 pages. v4: various improvements, more details