nLab
(infinity,1)-topos theory

Context

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

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

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

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 (,1)(\infty,1)-topos itself see the references at (∞,1)-topos.

Early frameworks for Grothendieck (as opposed to “elementary”) (,1)(\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 (,1)(\infty,1)-topos theory in terms of (∞,1)-category theory was given in

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

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