• DOI:10.1016/J.AIM.2004.05.004
Corpus ID: 119131806

Homotopical algebraic geometry. I. Topos theory.

@article{Toen2002HomotopicalAG,
  title={Homotopical algebraic geometry. I. Topos theory.},
  author={B. Toen and G. Vezzosi},
  journal={Advances in Mathematics},
  year={2002},
  volume={193},
  pages={257-372}
}

• B. Toen, G. Vezzosi
• Published 2002
• Mathematics
• Advances in Mathematics

This is the rst of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts. In this rst part we investigate a notion of higher topos. For this, we use S-categories (i.e. simplicially enriched categories) as models for certain kind of 1-categories, and we develop the notions of S-topologies, S-sites and stacks over them. We prove in particular, that for an S-category T endowed with an S-topology, there exists a model category of… Expand