English

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 \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.

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