# nLab elementary (infinity,1)-topos

### Context

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

(∞,1)-category theory

## Models

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

(∞,1)-topos theory

## Constructions

structures in a cohesive (∞,1)-topos

# Contents

## Idea

The notion of an elementary (∞,1)-topos is the analog of the notion of elementary topos in (∞,1)-category theory.

This is in contrast to the notion of an (∞,1)-topos equvialent to an (∞,1)-category of (∞,1)-sheaves, the analog of a sheaf topos, which is more specific.

## References

A proposal for a definition, with an eye towards homotopy type theory and the relation between type theory and category theory is on the very last slide of

This proposal is predicative, but could be made impredicative easily (to correspond closer to elementary 1-toposes rather than to types of 1-pretoposes) by adding a subobject classifier (i.e. a classifier for all subobjects, rather than merely the “classifiers for small subobjects” obtainable from object classifiers).

Revised on May 15, 2012 19:09:12 by Urs Schreiber (82.172.178.200)