nLab
higher topos theory

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.

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

Related concepts

• (0,1)-topos

• topos theory, topos

• 2-topos theory, 2-topos

• n-topos

• (∞,1)-topos theory, (∞,1)-topos

• higher topos theory

References

• Michael Shulman, n-topos for large n .