## October 13, 2009

### 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:

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 $(\infty,1)$-topos is 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.

Posted at October 13, 2009 1:15 AM UTC

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

Ah, so you’re no longer in Bonn?

Posted by: Kevin Lin on October 13, 2009 4:49 PM | Permalink | Reply to this

Ah, so you’re no longer in Bonn?

Currently I am oscillating back and forth. Luckily there is a good train connection.

I did certainly miss your GW-seminar today, unfortunately. I should be available at the elliptic seminar tomorrow, though.

Posted by: Urs Schreiber on October 13, 2009 5:08 PM | Permalink | Reply to this

GW-seminar

Posted by: Toby Bartels on October 13, 2009 11:35 PM | Permalink | Reply to this

### entries on Gromov-Witten invariants

It was supposed to and now does point to the $n$Café entry called A Seminar on Gromov-Witten Invariants – whose point is to attract contributors to the entry $n$Lab:Gromov-Witten invariants.