# nLab (infinity,1)-topos theory

### Context

#### $(\infty,1)$-Category theory

(∞,1)-category theory

## Models

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

(∞,1)-topos theory

## Constructions

structures in a cohesive (∞,1)-topos

# Contents

## Idea

The theory of (∞,1)-toposes, generalizing topos theory from category theory to (∞,1)-category theory.

## References

For origins of the notion of $(\infty,1)$-topos itself see the references at (∞,1)-topos.

Early frameworks for Grothendieck (as opposed to “elementary”) $(\infty,1)$-topoi are due Charles Rezk and ToënVezzosi in two versions (preprints 2002), via simplically enriched categories and via Segal categories:

A general abstract conception of $(\infty,1)$-topos theory in terms of (∞,1)-category theory was given in

The analog of the Elephant for $(\infty,1)$-topos theory is still to be written.

Revised on May 23, 2011 02:10:16 by Stephen Britton (75.64.180.220)