Characterizing algebraic stacks
Algebraic Topology
2007-08-21 v1 Category Theory
Abstract
We extend the notion of algebraic stack to an arbitrary subcanonical site C. If the topology on C is local on the target and satisfies descent for morphisms, we show that algebraic stacks are precisely those which are weakly equivalent to representable presheaves of groupoids whose domain map is a cover. This leads naturally to a definition of algebraic n-stacks. We also compare different sites naturally associated to a stack.
Cite
@article{arxiv.0708.2705,
title = {Characterizing algebraic stacks},
author = {Sharon Hollander},
journal= {arXiv preprint arXiv:0708.2705},
year = {2007}
}
Comments
12 pages, to appear in Proc. Amer. Math. Soc