### Path-Structured Smooth (∞,1)-Toposes

#### Posted by Urs Schreiber

It seems that this Friday I’ll give a talk to the group of Ieke Moerdijk, where I just started a new position (as I mentioned).

Over on the $n$Lab I am preparing some notes along which such a talk might proceed:

Posted at October 13, 2009 1:15 AM UTCPath-Structured Smooth $(\infty,1)$-Toposes (wiki page)

Abstract.A smooth topos is a context in which (synthetic) differential geometry exists. An $(\infty,1)$-topos is a context in which higher groupoids exist. Merging these two concepts yields the notion of a smooth $(\infty,1)$-topos: a context in which $\infty$-Lie groupoids exist.A lined topos is a context in which each space has a notion of path. A

path-structured smooth $(\infty,1)$-toposis a context in which each $\infty$-Lie groupoid comes with its smooth path $\infty$-groupoid, naturally.Path-structured and smooth $(\infty,1)$-toposes are the context in which gauge fields given by principal $\infty$-bundles with connection exist.

## Re: Path-Structured Smooth (∞,1)-Toposes

Ah, so you’re no longer in Bonn?