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- Discussion Type
- discussion topicNew page: G-norms
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jul 13th 2010

You can turn a set into a topological abelian group by equipping it with a family of G-pseudonorms.

- Discussion Type
- discussion topic0-site
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by TobyBartels
- Last Active Jul 13th 2010

shouldn’t 0-site be named (0,1)-site?

- Discussion Type
- discussion topic(2,2)-sheaves, or, Baković's 2-espaces étalé
- Category Latest Changes
- Started by DavidRoberts
- Comments 4
- Last comment by DavidRoberts
- Last Active Jul 13th 2010

Does anyone have any notes, or know of anyone who has notes, from Igor’s Oberwolfach or Utrecht talks?

- Discussion Type
- discussion topicFreyd cover
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by Todd_Trimble
- Last Active Jul 12th 2010

Began Freyd cover. What’s it for?

- Discussion Type
- discussion topic2-site
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Mike Shulman
- Last Active Jul 10th 2010

created 2-site with the material from Mike’s web (as he suggested). Added pointers to original articles by Ross Street.

- Discussion Type
- discussion topicPlethysm
- Category Latest Changes
- Started by John Baez
- Comments 55
- Last comment by Todd_Trimble
- Last Active Jul 10th 2010

I started a stub on plethysm.

Does anyone know how this mathematical term originated? I hear someone suggested it to Littlewood. But who? And why? And what’s the etymology, exactly?

- Discussion Type
- discussion topiclocally finitely presentable categories
- Category Latest Changes
- Started by John Baez
- Comments 17
- Last comment by Todd_Trimble
- Last Active Jul 10th 2010

- I have a query for Mike, or anyone who wants to tackle it, over at locally finitely presentable category. Mike seems to be saying that only the category of models of a
*finitary*essentially algebraic theory is locally finitely presentable, but some paper seems to suggest otherwise...

- Discussion Type
- discussion topic3-groupoid
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Eric
- Last Active Jul 10th 2010

tried to polish 3-groupoid a little

- Discussion Type
- discussion topicMore new pages
- Category Latest Changes
- Started by TobyBartels
- Comments 6
- Last comment by TobyBartels
- Last Active Jul 9th 2010

- Discussion Type
- discussion topicSchur functors
- Category Latest Changes
- Started by John Baez
- Comments 87
- Last comment by Todd_Trimble
- Last Active Jul 9th 2010

I’m struggling to further develop the page on Schur functors, which Todd and I were building. But so far I’ve only done a tiny bit of polishing. I deleted the discussion Todd and I were having near the top of the page, replacing it by a short warning that the definition of Schur functors given here needs to be checked to see if it matches the standard one. I created a page on linear functor and a page on tensor power, so people could learn what those are. And, I wound up spending a lot of time polishing the page on exterior algebra. I would like to do the same thing for tensor algebra and symmetric algebra, but I got worn out.

In that page, I switched Alt to $\Lambda$ as the default notation for exterior algebra. I hope that’s okay. I think it would be nice to be consistent, and I think $\Lambda$ is most widely used. Some people prefer $\bigwedge$.

- Discussion Type
- discussion topicNew pages and terminology clashes
- Category Latest Changes
- Started by Stephen Britton
- Comments 22
- Last comment by Stephen Britton
- Last Active Jul 9th 2010

- Hello everyone

I am new the nForum and have been informed that my additions to the nLab have introduced terminology clashes and could disrupt the coherence of the nLab. My sincerest apologies to anyone who could be negatively effected. The new pages I introduced follow:

* AbTop

* AbTor

* Alg(T)

* Aut

* Ban

* Beh

* BiComp

* BiTop

* Bij

* BooRng

* BooSpa

* Bor

* CAT

* CAT(X)

* CPO

Also started added pages after reading the nLab page 'database of categories'.

- Discussion Type
- discussion topiccenter of an abelian category
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jul 8th 2010

I have created a new entry center of an abelian category. Maybe it is superfluous as it is just a special case of a construction at center. However in this context there isa number of special theorems which I plan to enter at some point later, so maybe it is not an error to have a separate entry.

- Discussion Type
- discussion topicNew stub: prime numbers
- Category Latest Changes
- Started by TobyBartels
- Comments 7
- Last comment by Ian_Durham
- Last Active Jul 8th 2010

- Discussion Type
- discussion topicPlanar Algebra
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by Urs
- Last Active Jul 8th 2010

Began planar algebra for no very good reason.

- Discussion Type
- discussion topicreal closed field
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Jul 6th 2010

I wrote the beginnings of an article real closed field. I also wrote fundamental theorem of algebra, giving the proof essentially due to Artin which applies generally to real closed fields. Lucky for me, Toby recently wrote quadratic formula! :-)

Things like this have a tendency of spawning a bunch of new articles, but I left out a bunch of potential links in these articles. Please feel free to insert some!

- Discussion Type
- discussion topicsemialgebraic set
- Category Latest Changes
- Started by Todd_Trimble
- Comments 2
- Last comment by zskoda
- Last Active Jul 6th 2010

I wrote semialgebraic set. This should spawn other entries such as o-minimal structure.

- Discussion Type
- discussion topiccohomological descent
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by zskoda
- Last Active Jul 6th 2010

New entry cohomological descent.

- Discussion Type
- discussion topicMore locale theory articles
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by TobyBartels
- Last Active Jul 3rd 2010

- Discussion Type
- discussion topicNew page: nuclei
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jul 1st 2010

- Discussion Type
- discussion topicMore Stone Spaces stubs
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jul 1st 2010

Coming back to my project of working through

*Stone Spaces*, here are some rather blasé stubs: irreducible closed subspace, T-D-space, upper interval topology.

- Discussion Type
- discussion topicMore abstract nonsense: too simple to be simple
- Category Latest Changes
- Started by TobyBartels
- Comments 16
- Last comment by Ian_Durham
- Last Active Jul 1st 2010

Some things are too simple to be simple.

- Discussion Type
- discussion topicNew page: zero-divisors
- Category Latest Changes
- Started by TobyBartels
- Comments 6
- Last comment by TobyBartels
- Last Active Jun 30th 2010

Enjoy zero-divisor.

- Discussion Type
- discussion topicStuff
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by John Baez
- Last Active Jun 30th 2010

I’ve redirected the new article stuff to stuff, structure, property, because all of that stuff (pun not originally intended, but kept with delight) is already there, and it didn’t seem like the author knew about it. It doesn’t have to be that way, however, so move stuff > history back to stuff if you disagree, but then make some prominent links between the articles too.

- Discussion Type
- discussion topicDo the terms C-linear and *-categories already exist on the nLab?
- Category Latest Changes
- Started by Tim_van_Beek
- Comments 34
- Last comment by Urs
- Last Active Jun 29th 2010

A $\mathbb{C}-$linear category is simply a category where every Hom(x, y) is a complex vector space and the composition of morphisms is bilinear. A *-category is a $\mathbb{C}-$linear category that has a *-operation on each Hom(x, y) (same axioms a for a *-algebra) and a $C^*-$category further has a norm on each Hom(x, y) that turns it into a Banach space with $s^* s = |s|^2$ and $|st| \leq |s| |t|$ for all arrows s, t (s and t composable).

Is there already a page on the nLab that describes this structure?

- Discussion Type
- discussion topicleft Kan fibration
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Jun 27th 2010

the entry fibrations of quasi-categories was getting too long for my taste. I have to change my original plans about it.

Now I split off left Kan fibration from it, which currently duplicates material from this entry and from fibration fibered in groupoids. I'll see how to eventualy harmonize this a bit better.

Presently my next immediate goal is to write out as a pedagogical introduction to the notion of left/right fibration a nice detailed proof for the fact that a functor is an op-fibration fibered in groupoids precisely if its nerve is a left Kan fibration.

I wanted to do that today, but got distracted. Now I am getting too tired. So I'll maybe postpone this until tomorrow...

- Discussion Type
- discussion topicyoung diagram, various groups
- Category Latest Changes
- Started by John Baez
- Comments 7
- Last comment by Todd_Trimble
- Last Active Jun 26th 2010

I added material to Young diagram, which forced me to create entries for special linear group and special unitary group. I also added a slight clarification to unitary group.

I would love it if someone who knows algebraic geometry would fix this remark at general linear group:

Given a commutative field $k$, the

**general linear group**$GL(n,k)$ (or $GL_n(k)$) is the group of invertible $n\times n$ matrices with entries in $k$. It can be considered as a subvariety of the affine space $M_{n\times n}(k)$ of square matrices of size $n$ carved out by the equations saying that the determinant of a matrix is zero.In fact it’s ’carved out’ by the

*inequality*saying the determinant is*not*zero… so its description as an algebraic variety is somewhat different than suggested above. Right???

- Discussion Type
- discussion topicBibundle
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by Urs
- Last Active Jun 26th 2010

Started on bibundles, but there seem to be a raft of competing definitions. Perhaps they're all special cases of a most general definition.

- Discussion Type
- discussion topicA-model
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active Jun 26th 2010

started stub for A-model

- Discussion Type
- discussion topicmanifolds and cobordisms - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 26th 2010

started floating table of contents

- Discussion Type
- discussion topicharmonic form
- Category Latest Changes
- Started by Kevin Lin
- Comments 2
- Last comment by Urs
- Last Active Jun 26th 2010

- stub for harmonic form