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}
}
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
MODULI OF OBJECTS IN DG-CATEGORIES BY BERTRAND TOËN
On the homotopy theory of $n$-types
Au-dessous de SpecZ .
Moduli of objects in dg-categories
Model topoi and motivic homotopy theory
Categorical Foundations for K-theory
Augmented Homotopical Algebraic Geometry
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