This Is Not The n-Category Café

April 24, 2014 by

The n-Category Café is located at We only keep this site as a backup for the odd occasion when the main site goes down.


January 2, 2014 by

This is a test of a GIF with a background image.

Main Site Temporarily Down

January 6, 2012 by

The n-Category Café is located at We keep this site as a reserve in case anything goes wrong.

The main site will be temporarily down for 48 hours starting at 6pm Central Standard Time on Friday 6 January. In Greenwich Mean Time, that’s midnight at the end of 6 January and the beginning of 7 January. They’re shutting off the power to the building at the University of Texas where the server lives.

The Scottish Category Theory Seminar

May 5, 2010 by

The Scottish Category Theory Seminar is a newish series of occasional afternoon meetings, at locations roaming around the country (though there’ll probably never be any on highland mountaintops or remote misty lochs…). I’m very pleased to announce the second meeting of the seminar, in Edinburgh on 21 May.

We’ve worked hard to get a good mixture of mathematicians on the one hand, and theoretical computer scientists on the other. Two of the speakers, Antony Maciocia and Peter Kropholler, are mathematicians — Maciocia is in algebraic geometry, and Kropholler at the intersection of group theory and topology. The other two, Dirk Pattinson and Thorsten Altenkirch, are in theoretical computer science — though their talks should definitely be interesting to mathematicians.

All the speakers have been firmly requested to make their talks broadly accessible to what we hope will be a very mixed audience. So I’m looking forward to an excellent afternoon.

Here are the talks. To see the abstracts, click on the titles.

Incidentally, I think the Glasgow speaker has been inspired by some other talks in Glasgow…

If you think you’d like to come, send a mail to me (T.Leinster#maths,gla,ac,uk) or scotcats#cis,strath,ac,uk. It’s not essential that you do so — you can just turn up — but it would help, and you definitely should if you’re intending to come for dinner.

Category Theory and Philosophy of Mathematics Today

May 2, 2010 by

Here’s an interesting series of talks, announced by Andrei Rodin on the category theory mailing list:

Category Theory and Philosophy of Mathematics Today
(a satellite event associated with the workshop Foundations of
mathematics: What and Why?, Paris, May 18 – June 25 ).

When: Three days: May 17, 2010 from 9 A.M. to 4 P.M, May 31, 2010 from 9.30 A.M. to 4 P.M, and June 14, 2010 from 9.30 A.M. to 6.30 P.M.

Where: Paris, Ecole Normale Supérieure (45, rue d’Ulm, 75005).  Salle “W” (staircase B, 3d floor): May 17, 31 and June 14 in the morning.   Salle Beckett (ground floor): June 14 afternoon.

Languages: French and English

Here’s the program:

le 17 mai / May 17 (ENS, salle “W”):

9h – 9h30 / 9 – 9.30 A.M.:
Andrei Rodin:
Welcoming address

9h30 – 10h50 / 9.30 – 10.50 A.M.
Yuri Manin
Languages of Mathematics

11h – 12h20 / 11A.M. – 12.20 P.M.
Christian Houzel (*)

12h20 – 14h  / 12.20 P.M. – 2 P.M.

14h-15h / 2 – 3 P.M.
René Guitart (Paris-Diderot)
Topos and Algebraic Universe

15h – 16h / 3 – 4 P.M.
Noson Yanofsky
On the Utility of Category Theory

le 31 mai / May 31 (ENS, salle “W”):

9h30 – 10h30  /  9.30 – 10.30 A.M.
Alberto Peruzzi (*)
Categorical philosophy, rather than philosophy of category theory

10h40 – 12h  /  10.40 A.M. – 12 P.M.
Jean Sallantin & Dominique Luzeaux
Ideosphères et mathèmes : utilisation d’outils catégoriques

12h – 14h  / 12 P.M. – 2 P.M.

14h – 15h  /  2 – 3 P.M.
Alain Prouté
On the link between topoi and the vernacular of mathematics

15h – 16h  / 3 – 4 P.M.
Andrei Rodin
Towards categorical foundations of geometry: a historical approach

le 14 juin / June 14: (ENS, salle “W”, salle Beckett)

9h30 – 10h50  /  9.30 – 10.50 A.M. (salle “W”)
Jean Bénabou
“Transcendent” methods in Category  Theory

11h – 12h  / 11 A.M. – 12 P.M. (salle “W”)
Marc Lachièze-Rey (CNRS & Paris-Diderot),
Catégories et physique: un example de la gravitation quantique

12h20 – 14h  /  12.20 P.M. – 2 P.M.

14h – 15h  /  2 – 3 P.M.  (salle Beckett)
Giuseppe Longo
L’esprit des categories et la vie

15h – 16h  /  3 – 4 P.M. (salle Beckett)
Pino Rosolini (Genoa)
Categories and sets

16h15 – 17h15  / 4.15 – 5.15 P.M. (salle Beckett)
Jean Petitot

17h15 – 18h30  / 5.15 – 6.30 P.M. (salle Beckett)
Table Ronde / Round Table

(*) sous réserve d’une confirmation / to be confirmed

Hardware Problem

April 30, 2010 by

Golem, the computer on which the Cafe runs, has sadly passed away. A replacement should be up and running late next week – Jacques is working on it, for which we’re very grateful.

Until then, you can leave comments at the loose ends thread here.

Thanks again for your patience.

Update (6 May) The cafe is now visible again, but not fully operational. With any luck it will be working properly in a couple of days.

Normal Service is Resumed!

March 22, 2010 by

Thanks once more to the sterling work of Jacques Distler, the original Café is up and running again. So, please go there, rather than here, for all your mathematical, physical and philosophical needs.

The software problems seem to be mostly fixed. One or two people still find themselves unable to leave comments. If this happens to you, please tell me or one of the other hosts. We’ll post the comment for you and see if we can get the problem sorted out. (And if you just can’t wait to get that comment into cyberspace, you can put it at the loose ends entry at this site.)

Thanks for your patience.

Modeling Surface Diagrams

March 19, 2010 by

I’m currently at MSRI at a knot homology meeting. There are lots of people here with pictures of surfaces, some of these even being categorical, so I thought I would return to the subject of computer manipulation of these. In particular I thought I would make use of our (hopefully) brief sojourn at WordPress and take the opportunity to embed some videos.

Read the rest of this entry »

Intrinsic Volumes and Weyl’s Tube Formula (continued)

March 19, 2010 by

Tom Leinster was wanting to make some comments on my post Intrinsic Volumes and Weyl’s Tube Formula over at our usual place, so I’m just posting this to give him something to reply to.

Stack Semantics

March 18, 2010 by

Today I’m blogging from Washington D.C., at the Annual Meeting of the Association for Symbolic Logic. The ASL is mostly populated with material set theorists and classical logicians, but this year they had a special session on Categorical Logic, and another one on Logic and the Foundations of Physics (including lots of categorical quantum mechanics)—a promising sign for the recognition of category theory. I was invited to speak at the former session this afternoon, about stack semantics and 2-categorical logic.

And not-entirely-coincidentally, at long last I’ve put online a draft of my (first) paper about the stack semantics and comparing material and structural set theories. You can get it from my nlab page:

There are also slides from today’s talk and one from last November.

In brief, the idea of the stack semantics is to extend the internal logic of a topos to a language which can talk about unbounded quantifiers (quantifiers of the form “for all sets” rather than “for all elements of A” for some fixed set A). In this extended language, we can then state topos-theoretic axiom schemas which are as strong as the full separation and replacement axioms of ZF. (Ordinary topos theory is only equiconsistent with bounded Zermelo set theory, which is much weaker than ZF.) This generalization is extremely easy—even easier than some presentations of the ordinary internal logic—and is in fact implicit throughout topos theory, but has seemingly never been written down precisely before.

If that intrigues you, then you may want to look first at the talk from November; it’s aimed at category theorists without much experience in categorical logic. Then you can go on to look at the paper itself, most of which should (I hope) also be fairly accessible. Comments are welcome!

Note: This entry and its comments have been copied back to the main n-Category Cafe site. Please submit further comments there (unless the comment system there starts to have issues again).