# 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: “geometric homotopy theory”.

## References

An quick introduction is in part 3, 4 of

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 via model categories

and due to 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.

Last revised on June 11, 2018 at 08:36:53. See the history of this page for a list of all contributions to it.