Structured Spaces


Higher geometry

Higher algebra

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which develops the generalization of the notion of a ringed topos from topos theory to (∞,1)-topos theory and formulates basic notions of geometry in this context (“higher geometry”).

A 1-categorical precursor would be

  • Monique Hakim, Topos annelés et schémas relatifs, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 64, Springer, Berlin, New York (1972).

The theory is general, but the focus of the examples and applications is on derived algebraic geometry/E-∞ geometry.


A survey is at A Survey of Elliptic Cohomology - the derived moduli stack of derived elliptic curves in the section notions of space.


Revised on December 28, 2013 06:30:26 by Urs Schreiber (