nLab higher topos theory

Context

Topos Theory

Could not include topos theory - contents

$(\infty,1)$-Topos Theory

(∞,1)-topos theory

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 $(n,r)$-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 $(\infty, 1)$ case.

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

References

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