Higher stacks as diagrams
Algebraic Topology
2022-04-07 v2 Category Theory
Abstract
Several possible presentations for the homotopy theory of (non-hypercomplete) -stacks on a classical site S are discussed. In particular, it is shown that an elegant combinatorial description in terms of diagrams in S exists, similar to Cisinski's presentation, based on work of Quillen, Thomason and Grothendieck, of usual homotopy theory by small categories and their smallest (basic) localizer. As an application it is shown that any (local) fibered (a.k.a. algebraic) derivator over S with stable fibers extends to -stacks in a well-defined way under mild assumptions.
Cite
@article{arxiv.2105.08479,
title = {Higher stacks as diagrams},
author = {Fritz Hörmann},
journal= {arXiv preprint arXiv:2105.08479},
year = {2022}
}