# Homotopical algebraic geometry. I. Topos theory.

@article{Toen2002HomotopicalAG,
title={Homotopical algebraic geometry. I. Topos theory.},
author={Bertrand Toen and Gabriele Vezzosi},
year={2002},
volume={193},
pages={257-372}
}
• Published 2 July 2002
• Mathematics
281 Citations
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## References

SHOWING 1-10 OF 112 REFERENCES

• Mathematics
• 2004
This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutative
We give a model structure on the category of simplicial presheaves on some essentially small Grothendieck site T . When T is the Nisnevich site it specializes to a proper simplicial model category
The problem of constructing a nice smash product of spectra is an old and well-known problem of algebraic topology. This problem has come to mean the following: Find a model category, which is
• Mathematics
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These are expanded notes of some talks given during the fall 2002, about homotopical algebraic geometry with special emphasis on its applications to derived algebraic geometry and derived deformation
Contributing Authors. Preface. Part I: General surveys. Localizations W.G. Dwyer. 1. Introduction. 2. Algebra. 3. Homological localization in topology. 4. Localization with respect to a map. 5.
• Mathematics
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We develop homotopical algebraic geometry ([To-Ve 1, To-Ve 2]) in the special context where the base symmetric monoidal model category is that of spectra S, i.e. what might be called, after
We present a definition of homotopy algebra for an operad, and explore its consequences. The paper should be accessible to topologists, category theorists, and anyone acquainted with operads. After