nLab
higher topos theory

Context

Topos Theory

Could not include topos theory - contents

(,1)(\infty,1)-Topos Theory

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Contents

Idea

Higher topos theory is the generalisation to higher category theory of topos theory. It is partly motivated by Grothendieck’s program in Pursuing Stacks.

More generally, the concept (n,r)(n,r)-topos is to topos as (n,r)-category is to category.

Rather little is known about the very general notion of higher topos theory. A rich theory however exists in the context of (∞,1)-categories, as described in Jacob Lurie's book Higher Topos Theory, which only covers the (,1)(\infty, 1) case.

Just as the archetypical example of an ordinary topos (i.e. a (1,1)(1,1)-topos) is Set – the category of 0-categories – so the \infty-category of n-categories or at least of nn-groupoids should form the archetypical example of an (n+1,1)(n+1,1)-topos.

References

Revised on October 8, 2013 21:32:07 by David Corfield (87.115.31.43)