Gluing restricted nerves of $\infty$-categories

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 étale cohomology of schemes. Our results are applied in subsequent articles to construct Grothendieck's six operations in étale cohomology of Artin stacks.

54 pages. v4: various improvements, more details

References in corpus (2)

• Enhanced six operations and base change theorem for higher Artin stacks
• Gluing pseudo functors via $n$-fold categories

Cited by in corpus (4)

• A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula
• Enhanced adic formalism and perverse t-structures for higher Artin stacks
• Motivic Realizations of Singularity Categories and Vanishing Cycles
• Gluing pseudo functors via $n$-fold categories