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- Discussion Type
- discussion topicfirst order and BF-gravity
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 26th 2009

created stubs for gravity as a BF-theory and first-order formulation of gravity

- Discussion Type
- discussion topicsymplectic geometry and Hamiltonian mechanics
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 26th 2009

On request by David Corfield, I wrote a bit about symplectic geometry and classical hamiltonian mechanics

- Discussion Type
- discussion topicUC RIverside Seminar on Cobordism and Topological Field Theories
- Category Latest Changes
- Started by Bruce
- Comments 4
- Last comment by Urs
- Last Active Oct 25th 2009

- 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).

- Discussion Type
- discussion topicnew stub: Hilbert scheme
- Category Latest Changes
- Started by bwebster
- Comments 1
- Last comment by bwebster
- Last Active Oct 25th 2009

- I got tired off looking at a question mark on my personal web and added a stub for Hilbert schemes.

- Discussion Type
- discussion topicHasse diagram
- Category Latest Changes
- Started by Eric
- Comments 3
- Last comment by Eric
- Last Active Oct 25th 2009

I borrowed a nice description of Hasse diagrams from Toby.

- Discussion Type
- discussion topiccovering relation
- Category Latest Changes
- Started by Eric
- Comments 2
- Last comment by TobyBartels
- Last Active Oct 25th 2009

I weakened the definition of covering relation for directed graphs so that satisfy the covering relation if their is an edge and no other path from to . The condition that there is no with edges and is too strong.

- Discussion Type
- discussion topicFAQ section on personal pages
- Category Latest Changes
- Started by bwebster
- Comments 3
- Last comment by bwebster
- Last Active Oct 24th 2009

`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.`

- Discussion Type
- discussion topicTony Pantev and Ludmil Katzrakov
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 24th 2009

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)

- Discussion Type
- discussion topicLarry Breen
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 24th 2009

created page for Lawrence Breen

- Discussion Type
- discussion topicGrassmann algebra vs exterior algebra
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by Urs
- Last Active Oct 24th 2009

John put in a definition at Grassmann algebra. Should these be distinguished from exterior algebra?

- Discussion Type
- discussion topicmore on Cauchy completion
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Urs
- Last Active Oct 24th 2009

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.

- Discussion Type
- discussion topicUnitarity of induced representations
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 22nd 2009

Our new contributor Aaron F would like people to check this at induced representation.

- Discussion Type
- discussion topicJohan Louis Dupont
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Oct 22nd 2009

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)

- Discussion Type
- discussion topicMike Stay has written …
- Category Latest Changes
- Started by TobyBartels
- Comments 11
- Last comment by TobyBartels
- Last Active Oct 22nd 2009

- Discussion Type
- discussion topicRegular categories
- Category Latest Changes
- Started by amathew
- Comments 9
- Last comment by TobyBartels
- Last Active Oct 22nd 2009

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.

- Discussion Type
- discussion topicsite-dependence of model structure on simplicial presheaves
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Oct 22nd 2009

I started a section

dependence on the underlying site at model structure on simplicial presheaves.

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... :-)

- Discussion Type
- discussion topicbisimplicial object
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 20th 2009

created bisimplicial object with two useful props.

Also linked to it from simplicial object

- Discussion Type
- discussion topicsimplicial deRham complex
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Oct 20th 2009

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.

- Discussion Type
- discussion topicLars Kindler
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 20th 2009

Lars Kindler has joined to edit D-module.

- Discussion Type
- discussion topic$$(n,n+1)$$-categories
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Urs
- Last Active Oct 20th 2009

I mentioned these at higher category theory and (n,n)-category, where it had been implied that the latter were as far as one could go in increasing the second parameter.

- Discussion Type
- discussion topicmatrix mechanics
- Category Latest Changes
- Started by David_Corfield
- Comments 10
- Last comment by David_Corfield
- Last Active Oct 20th 2009

- Began entry with that name.

- Discussion Type
- discussion topicringoid
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by TobyBartels
- Last Active Oct 20th 2009

I think Ab-enriched category is a better name for the page than ringoid.

- Discussion Type
- discussion topic[[Jason Dusek]] joined and inspired me to start [[2-rig]].
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 20th 2009

Jason Dusek joined and inspired me to start 2-rig.

- Discussion Type
- discussion topicNew entry: [[poincare group]]
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by TobyBartels
- Last Active Oct 20th 2009

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.

- Discussion Type
- discussion topicWrote [[short map]] and expanded [[isometry]]. (n/t)
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 20th 2009

- Discussion Type
- discussion topicG-principal oo-bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 19th 2009

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?

- Discussion Type
- discussion topicRequest for Help
- Category Latest Changes
- Started by Andrew Stacey
- Comments 1
- Last comment by Andrew Stacey
- Last Active Oct 19th 2009

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).

- Discussion Type
- discussion topic[[two-valued topos]]
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Mike Shulman
- Last Active Oct 19th 2009

I wrote two-valued topos to help me tighten up Mike's latest edit to cocomplete well-pointed topos.

- Discussion Type
- discussion topicReply to Roger Witte at [[foundations]]. (n/t)
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 18th 2009

Reply to Roger Witte at foundations.

- Discussion Type
- discussion topicSch/S and S-Sch (notational point)
- Category Latest Changes
- Started by amathew
- Comments 3
- Last comment by zskoda
- Last Active Oct 18th 2009

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.