nLab (infinity,1)-topos theory



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

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

(∞,1)-topos theory

structures in a cohesive (∞,1)-topos



The theory of (∞,1)-toposes, generalizing topos theory from category theory to (∞,1)-category theory: “geometric homotopy theory”.


An quick introduction is in part 3, 4 of

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 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 (,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.

Last revised on March 13, 2019 at 11:06:15. See the history of this page for a list of all contributions to it.