English

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.

Keywords

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

R2 v1 2026-06-21T09:09:02.645Z