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

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

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

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

• 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?

• 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...
• 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 $\bigwedge$.

• 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'.
• 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.

• 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!

• 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.

• 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?

• 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...

• 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???

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