nLab
Structured Spaces

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Context

Higher geometry

higher geometry / derived geometry

Ingredients

Concepts

Constructions

Examples

Theorems

Higher algebra

higher algebra

universal algebra

Algebraic theories

Algebras and modules

Higher algebras

Model category presentations

Geometry on formal duals of algebras

Theorems

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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.

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).

Survey

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

Contents

Revised on December 20, 2012 05:07:21 by Urs Schreiber (82.169.65.155)
Edit | Back in time (5 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: classifying topos, smooth algebra, Jacob Lurie, derived stack, structured (infinity,1)-topos, derived smooth manifold, algebraic geometry, geometry (for structured (infinity,1)-toposes), space, 2009 September changes, higher geometry, generalized scheme, Deligne-Mumford stack, n-localic (infinity,1)-topos, derived scheme, derived Deligne-Mumford stack, scheme as a locally affine structured (infinity,1)-topos, ringed topos, A Survey of Elliptic Cohomology - the derived moduli stack of derived elliptic curves, derived group scheme, applications of (higher) category theory, etale geometric morphism, smooth manifold, derived geometry, locally representable structured (infinity,1)-topos, over-(infinity,1)-topos, cohesive (infinity,1)-topos -- structure sheaves, locally ringed topos, essentially algebraic (infinity,1)-theory, locally algebra-ed topos, cohesive (infinity,1)-topos -- infinitesimal cohesion, Bohr topos, classifying (infinity,1)-topos, Monique Hakim