# nLab higher topos theory

Contents

topos theory

## Theorems

#### $(\infty,1)$-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, see at (∞,1)-topos theory

## Examples

### Flavors of higher toposes

flavors of higher toposes

### Archetypical higher toposes

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,r)-categories should form the archetypical example of an $(n+1,r+1)$-topos:

###### Example

(examples of archetypical higher toposes)

## References

Last revised on August 25, 2021 at 11:38:24. See the history of this page for a list of all contributions to it.