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- Discussion Type
- discussion topicmonomorphism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 27th 2009

expanded the previously pitiful monomorphism

- Discussion Type
- discussion topicMorphisms of graphs
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 27th 2009

Discussion resumes at the bottom of graph.

- Discussion Type
- discussion topicmodel category theory - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 26th 2009

started model category theory - contents and added this as floating toc to relevant entries

- Discussion Type
- discussion topicPlebanski formulation of gravity
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 26th 2009

Added some references to Plebanski formulation of gravity

- 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.

- Discussion Type
- discussion topicMinor changes (Hecke algebra, Hilbert basis theorem, additive envelope, etc.)
- Category Latest Changes
- Started by amathew
- Comments 4
- Last comment by JonAwbrey
- Last Active Oct 17th 2009

- I added a description of the degenerate affine Hecke algebra to the Hecke algebra page as one of the many variants.

I added the categorical generalization of Schur's lemma to that page.

I wrote a short stub on the additive envelope of a category, which Mike Shulman has expanded.

I mentioned the generalization of the Morse lemma to Hilbert manifolds.

I added the generalization of Hilbert's basis theorem to the case of where the ground ring is noetherian (not necessarily a field).

I wrote a short page on the Eilenberg swindle.

- Discussion Type
- discussion topicAkil Mathew
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Todd_Trimble
- Last Active Oct 17th 2009

I see that Akil Mathew has worked on a bunch of entries. Great! We should try to contact him and ask hom to record his changes here.

- Discussion Type
- discussion topicA-oo category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 17th 2009

Expanded the "Idea" section at A-infinity category.

- Discussion Type
- discussion topiccup product
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 17th 2009

Expanmded the idea section at cup product

- Discussion Type
- discussion topic[[Hugh Thomas]] joined to edit [[quiver]] (n/t)
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by Urs
- Last Active Oct 16th 2009

Hugh Thomas joined to edit quiver

- Discussion Type
- discussion topicthis and that
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 16th 2009

I added Alex's recent lecture notes to cobordism hypothesis and in that process polished some typesetting there slightly.

Then I was pleased to note that Noah Snyder joined us and worked on fusion category. I created a page for him.

- Discussion Type
- discussion topiccocomplete well-pointed topos
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by TobyBartels
- Last Active Oct 15th 2009

Wrote a proof at cocomplete well-pointed topos that characterizes Grothendieck universes and Set.

- Discussion Type
- discussion topicessential image
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Oct 15th 2009

I don't think that the (non-full) essential image of an arbitrary functor is well-defined.

- Discussion Type
- discussion topicfivebrane 6-group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 15th 2009

created fivebrane 6-group with the idea

- Discussion Type
- discussion topicexamples for smooth toposes
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 15th 2009

I added a fairly long (but still immensely incomplete) examples section to smooth topos.

I mention the "well adapted models" and say a few words about the point of it. Then I have a sectoin on how and in which sense algebraic geometry over a field takes place in a smooth topos. here the model is described easily, but I spend some lines on how to think of this. In the last example sections I have some remarks on non-preservation of limits in included subcategories of tame objects, but all that deserves further expansion of course.

- Discussion Type
- discussion topiceffects of foundations on "real" mathematics
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by JonAwbrey
- Last Active Oct 15th 2009

created effects of foundations on "real" mathematics and linked to it from foundations.

This is to archive an exchange between Toby and James on the blog here. The hope would be that eventually the list of examples is expanded here.

- Discussion Type
- discussion topicsmooth topos database
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 15th 2009

started filling in material into the planned database of smooth toposes at Models for Smooth Infinitesimal Analysis.

- Discussion Type
- discussion topicorthogonal group... in a lined topos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 15th 2009

I continued working my way through the lower realms of the Whitehead tower of the orthogonal group by creating special orthogonal group and, yes, orthogonal group.

For the time being the material present there just keeps repeating the Whitehead-tower story.

But I want more there, eventually: I have a query box at orthogonal group. The most general sensible-nonsense context to talk about the orthogonal group should be any lined topos.

I am wondering if there is anything interesting to be said, from that perspective. Incidentally, I was prepared in this context to also have to create general linear group, only to find to my pleasant surprise that Zoran had already created that some time back. And in fact, Zoran discusses there an algebro-geometric perspective on GL(n) which, I think, is actually usefully thought of as the perspective of GL(n) in the lined topos of, at least, presheaves on .

Presently I feel that I want eventually a discussion of all those seemingly boring old friends such as and and etc. in lined toposes and smooth toposes. Inspired not the least by the wealth of cool structure that even just carries in cases such as the -topos in Models for Smooth Infinitesimal Analysis.

- Discussion Type
- discussion topicFivebrane group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 14th 2009

created Fivebrane group but was being lazy:

essentially copy-and-pasted the intro from String group and then left a link to Fivebrane structure.

Then I went through String structure and Fivebrane structure and added links to String group and Fivebrane group.

- Discussion Type
- discussion topicHaynes Miller
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 14th 2009

created a page for Haynes Miller, since I just mentioned his name at string group as the one who coined that term.

not much on the page so far. Curiously, I found only a German Wikipedia page for him

- Discussion Type
- discussion topiciTeX - LaTeX differences in the FAQ
- Category Latest Changes
- Started by Andrew Stacey
- Comments 1
- Last comment by Andrew Stacey
- Last Active Oct 14th 2009

I've started listing differences between iTeX and LaTeX in the FAQ. That seemed the most logical place (I don't think we want a proliferation of places where users should look to find simple information) so either here or the HowTo seemed best. I chose the FAQ because the most likely time someone is going to look for this is when they notice something didn't look right.

The issue is that whilst iTeX is meant to be close to LaTeX they are

**never**going to be the same so it's worth listing known differences with their work-arounds.So far I've noted operator names, whitespace in

`\text`

, and some oddities on number handling.

- Discussion Type
- discussion topichomotopy group (of an oo-stack)
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 13th 2009

created homotopy group (of an infinity-stack)

a bit rough for the time being.

Also added a suitable link and short remark at homotopy group.

- Discussion Type
- discussion topicVishal Lama
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 13th 2009

Vishal Lama joined the Lab!

on his page he promises to create Lab pages on some books on category theory and topos theory. Great, I am looking forward to it

- Discussion Type
- discussion topicpath-structured smoth (oo,1)-toposes
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Oct 13th 2009

started working on

schreiber:path-structured (infinity,1)-toposes

This is a kind of survey of some constructions I've recently been spamming the nLab with.

- Discussion Type
- discussion topicQuestions on foundations
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 13th 2009

Roger Witte asks a question at foundations that looks interesting but which I haven't really thought about yet.

- Discussion Type
- discussion topicTodd wrote …
- Category Latest Changes
- Started by TobyBartels
- Comments 8
- Last comment by Todd_Trimble
- Last Active Oct 12th 2009

- Discussion Type
- discussion topicstructural meaning of [[axiom of foundation]]
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 12th 2009

I added a paragraph on structural meaning to axiom of foundation.

- Discussion Type
- discussion topicnLab on nLab
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by TobyBartels
- Last Active Oct 12th 2009

I added the Lab itself to Online Resources, since that list is getting a lot of attention and may well be copied to other contexts.

- Discussion Type
- discussion topicRedirection redirection
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 11th 2009

I moved the redirect for de Rham cohomology from differential form to de Rham complex.

- Discussion Type
- discussion topic[[Gram-Schmidt process]]
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 10th 2009

Todd just wrote Gram-Schmidt process; I added a bit.

- Discussion Type
- discussion topicMoved biography to people
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Urs
- Last Active Oct 10th 2009

As planned here