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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• I made a UC Riverside Seminar on Cobordism and Topological Field Theories page to record all the notes from the seminar. Kind of like a seminar webpage, but in the nLab. Heh, I'm at home so I can't post comments to the n-category cafe (I'm trying to sort this out, my computer is not allowed to post comments currently).
• I got tired off looking at a question mark on my personal web and added a stub for Hilbert schemes.
• I weakened the definition of covering relation for directed graphs so that $(x,y)$ satisfy the covering relation if their is an edge $x\to y$ and no other path from $x$ to $y$. The condition that there is no $z$ with edges $x\to z$ and $z\to y$ is too strong.

• This comment is invalid XML; displaying source. Following discussion here <a href="http://www.math.ntnu.no/~stacey/Vanilla/nForum/comments.php?DiscussionID=244&page=1#Item_3" >here</a>, I decided it made sense to have an <a href="http://ncatlab.org/nlab/show/FAQ#how_can_i_get_a_personal_section_of_the_nlab_14" >FAQ entry on personal pages.</a> It doesn't say much at the moment, but I guess the only important piece of information is that you have to write Urs.
• created pages for Tony Pantev and Ludmil Katzarkov

(not much there yet, am just following the idea that it would be nice that most authors whose references are cited in some entry also have a page with at least a link to their website)

• I added the case of Set-enriched category theory to the example section of Cauchy complete category (thanks to David Corfield for fixing my LaTeX errors), and inserted the definition at Karoubi envelope. There is an issue of choosing how to split idempotents which someone like Toby might want to say something about.

• created page for Johan Louis Dupont, cited at simplicial deRham complex

(given that at that entry I am trying to merge some of Dupont's work with some of that of Anders Kock, it is curious that JL Dupont and Anders Kock are decade-long colleagues in Aarhus, as Anders Kock kindly reminds me a minute ago)

• To the entry on [[regular category]] I added a brief note describing an application of this idea and the calculus of relations to a paper of Knop. For the future I will try to flesh this note out as well as add a page on tensor categories.

By the way, does the definition of a tensor category have to include linearity? It seems that the definitions vary depending on where one looks (e.g. whether the monoidal structure is an additive functor). Thanks.

• I started a section

So far this quotes a result from Jardine's lectures and then looks a bit at an example.

At that example I would really like to conclude that the Quillen adjunction discussed there is actually a Quillen equivalence. But I have to interrupt now to make a telephone call... :-)

• I started an entry simplicial deRham complex

on differential forms on simplicial manifolds.

In parts this is for me to collect some standard references and definitions (still very incomplete on that aspect, help is appreciated -- is there a good reference by Dupont that is online available?)

and in parts this is to discuss the deeper abstract-nonsense origin of this concept.

I am thinking that

• with differential forms understood in the synthetic context as just the image under Dold-Kan of the cosimplicial algebra of functions on the simplicial object of infinitesimal simplices in some space

• it follows that the simplicial deRham complex of a simplicial object is just the image under Dold-Kan of the cosimplicial algebra of functions on the realization of the bisimplicial object of infinitesimal simplices in the given simplicial space.

This looks like it is prretty obvious, once one stares at the coend-formula, but precisely that makes me feel a bit nervous. Maybe i am being too sloppy here. Would appreciate you eyeballing this.

• Began entry with that name.
• I wrote Poincare group as an entree to the project of carrying on in nLab the blog discussion on unitary representations of the Poincare group. I'm not a specialist of course, so I ask the experts to please examine for accuracy.

• I expanded and polished the discussion of the abstract definition of of G-principal oo-bundles in an arbitrary (oo,1)-topos at principal infinity-bundle.

Parts of this could/should eventually be moved/copied to action and action groupoid, but I won't do that now.

I'd be interested in comments. One would expect that for the case that the ambient (oo,1)-topos is Top this style of definition should be well known in the literature, but I am not sure if it is. In fact, the examples listed further below in the entry, (the construction by Quillen and the Stasheff-Wirth construction) seems to indicate that this very simple very general nonsense picture has not been conceived as such before. Could that be true?

• I've removed the request for help link from the main contents. It didn't get used much (though I got answers to my questions there!). Since we have yet to actually delete a page, rather than just blank the request for help page I've put a pointer to where one can ask questions (pretty similar to that on the FAQ).

• I created a page for S-Sch as a notation for S-schemes to refer to in another post. Zoran pointed out that the notation is nonstandard (I do not know why I thought it was normal) and changed the title to [[Sch/S]]. I thus changed the first sentence to read Sch/S instead.