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

• It got announced in another category, but here it is in Latest Changes:

Todd began (and then I edited) simple group.

• I wrote a quick entry conformal group, just from memory. Somebody could check and expand. In fact it would not be bad to have also a separate entry on conformal and on quasiconformal mappings.

• somehow I missed that there already is a page compact operator and created compact operators. The plural is another error :-) the unsatisfied link that I used to create the page was “compact operators”. When I tried to rename it to the singular term it failed, of course. Now the page compact operators is simply superfluous, but as a non-administrator I cannot delete it…

• Created sequential compactness, should probably link to all these compactness variations from compact space. Not sure if I got the “iff” bit right in the relationship with compactness itself; will check it myself if no-one fixes it in the meantime.

I decided that this was the key property in manifolds of mapping spaces and to stop trying to figure out a Froelicher version of sequentially compact for the time-being.

• the term “twist” or “twisted” is one of those insanely ambiguous terms in math. Trying to follow our recent agreement on how to deal with ambiguous page names, I tried to indicate this at twist .

• Created lax-idempotent 2-monad, with some definitions from Kelly–Lack. I think Kock has a couple of others. I’ll add more, like proofs of the equivalence of the definitions, and more on the cocompletion example, later (next week, probably).

• The final copy of my thesis is up on the lab. Available from Fundamental Bigroupoids and 2-Covering Spaces. I’ve fixed the typo in definition 5.1 that made it into the print copy ;)

Now to all the other projects that are on the back burner, time permitting…

• stub for 2-topos (mostly so that the links we have to it do point somewhere at least a little bit useful)

• started a floating toc for topos theory. See at the right of topos.

Please feel encouraged to expand and improve the structure.

• I have made a comment on the groupoid cardinality page. It draws peoples attention to Quinn's notes on TQFTs which uses a notion of homotopy order to construct scaling factors in a simple TQFT. This does not seem to be mentioned in stuff that I have seen and googling gets very few hits for this. It is clearly the same as groupoid cardinality when both are defined.
• finally noticed that (infinity,1)-sheaf was hardly even a stub. Have now filled some genuine content in there.

• Created free monad with a discussion of some of the subtleties and the notion of “algebraically-free”.

• I’ve started porting my notes “differential topology of loop spaces” over to the nlab, starting at differential topology of mapping spaces. As part of the transfer, I intend to map out the theory for general mapping spaces, not just loop spaces (that’ll give me a bit more motivation to do the transfer since just cut-and-paste is boring!). I’ve just copied over the contents and the introduction so far and haven’t edited them as yet. In particular, although I’ve wikilinked all the original section names, these will get changed as they currently focus on loop spaces.

The introduction to the original document ended as follows (not copied over to the new version):

This document began life as notes from talks given at NTNU and at Sheffield so I would like to thank the topologists at those institutions, and in particular Nils Baas, for letting me talk about my favourite mathematical subject. I would also like to thank Ralph Cohen and the “loop group” at Stanford.

This is by no means a ﬁnished document, as an example it is somewhat sparse on references. Any comments, suggestions, and constructive criticism will be welcomed.

The second paragraph is sort-of stating the obvious as it holds to some extent for any nLab page! And I would love to be able to add some more names to the list in the first paragraph. Again, I hope it goes without saying but I’ll say it anyway: although I anticipate being the main contributor to these pages, it is not my project! I would love it if people read it, add comments, add other stuff, write (constructive) graffiti, link it to other stuff.

• The entry cover was in a pitiful state. I tried to brush it up a bit. But I am afraid I am still not doing it justice. But also I don’t quite have the leisure for a good exposition right now. What I really want is to create an entry good cover in a moment…

• stub for Sullivan construction (I got annoyed that the entry didn’t exist, but also don’t feel like doing it justice right now)

• Because I want to point to it in a reply to the current discussion on the Category Theory Mailing list, I tried to brush up the entry k-tuply monoidal n-category a bit.

In particular I

• expanded the Idea section and added some statements that had been missing there;

• reacted to the old query box discussion there and moved the query box to the very bottom;

• added a section on k-tuply monoidal $\infty$-groupoids and $\infty$-stacks here.

• added a section on k-tuply monoidal $(n,1)$-categories here

• I had started an article on AT category (which I originally mis-titled as “AT categories” – thank you Toby for fixing this!), but getting a little stuck here and there. I’m using the exchange between Freyd and Pratt on the categories mailing list (what else is there?) as my reference, but as is so often the case, Freyd’s discussion is a little too snappy and terse for me to follow it down to all the nitty-gritty details.

There’s a minor point I’m having trouble verifying: that coproducts are disjoint (as a consequence of the AT axioms that Freyd had enunciated thus far where he made that claim, in his main post), particularly that the coprojections are monic. Presumably this isn’t too hard and I’m just being dense. A slightly less than minor point: I’m having trouble verifying Ab-enrichment of the category of type A objects. I believe Freyd as abelian-categories-guru implicitly – I don’t doubt him. Can anyone help?

• polished a bit and expanded a bit at interval category (nothing deep, just so that it looks better)

• Todd is helping me understand opposite categories beginning with $FinSet^{op}$ here.

This discussion helped prompt some improvement of the page opposite category. When I look at that page now, I see the statement:

The idea of noncommutative geometry is essentially to define a category of spaces as the opposite category of a category of algebras.

This reminded me of a remark I made in the “Forward” to a paper I wrote back in 2002, so I’ve now itexified that “Foreward” here:

Noncommutative Geometry and Stochastic Calculus

By the way, this also suggests that the category $FinSet$ is the category of spaces opposite to the category of finite Boolean algebras in the sense of space and quantity.

• I noticed that recently Konrad Waldorf created a very nice article

I went through it and added definition/theorem/proof-environments and lots of hyperlinks. Some of them are unsaturated. Maybe somebody feels inspired to create corresponding entries.