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I threw in some references to the early topos approach to set theory in ETCS. On this occasion I couldn’ t resist the temptation to rearrange somewhat the lay-out of the entry: actually I thought it better not to throw HOTT immediately at the reader and gave Palmgren’s ideas a proper subsection. I’ve also deflated a bit the foundational claims of ETCS sticking more to what appears to me to be Lawvere’s original intentions.
created essentially algebraic (infinity,1)-theory (just for completness, nothing unexpected there)
By the way, at essentially algebraic theory there is a pointer to “references below”, but no references are given.
started a hyperlinked index for the book Spin geometry
put a bare minimum into graded commutator, just because I needed to link to it.
wrote a bare minimum into Atiyah-Bott-Shapiro isomorphism.
<p>I created <a href="https://ncatlab.org/nlab/show/synthetic+differential+geometry+applied+to+algebraic+geometry">synthetic differential geometry applied to algebraic geometry</a> which is supposed to host a question that I am going to post on <a href="http://go2.wordpress.com/?id=725X1342&site=sbseminar.wordpress.com&url=http%3A%2F%2Fmathoverflow.net%2F">math Overflow</a> following the discussion we have of that <a href="http://sbseminar.wordpress.com/2009/10/14/math-overflow/#comment-6875">here at SBS</a>.</p>
<p>In that context I also wrote a section at <a href="https://ncatlab.org/nlab/show/algebraic+geometry">algebraic geometry</a> intended to describe the general-nonsense perspective. But that didn't quite find the agreement with Zoran and while we are having some discussion about this in private, he has restructured that entry now.</p>
started Calabi-Yau object. But am being interrupted…
brief entry on Turaev-Viro model, an entry long overdue. But for the moment it just records some references.
Bruce Bartlett has a comment on what is currently the last of these references and he will post it below in a moment…
am creating
listing the statements of the classification results, for the various cases. As far as I am aware of them.
gave 2d TQFT a slightly more informative Idea-section, highlighting the difference between the classical strict case classified by Frobenius algebras and the local/extended non-compact case classified by Calabi-Yau objects.
Added a reference by Abrams as a candidate for a first rigourous proof of the classification result via Frobenius algebras, and added citations for the local case (copied over from TCFT).
Created a stub at Milnor K-theory, which is now just an MO answer of Cisinski. To be expanded at some later point when I study this in more detail.
New page: n-types cover
wrote the first part of a discussion of prequantized Lagrangian correspondences, showing how traditional Hamiltonian and Lagrangian mechanics are naturally absorbed into the context of “local prequantum field theory” and “motivic quantization”.
Simple as it is, but does anyone know if the proposition in the section The classical action functional prequantizes Hamiltonian correspondences has been made explicit in the literature before? I can’t find it, but it should have been discussed before. If anyone has a citation, please let me know. Of course all the ingredients of the little proof are simple classical steps, but I am wondering if this has been observed as a statement, simple as it may be, on the prequantum lift of the more famous Lagrangian correspondences.
I added the redirect anomaly to quantum anomaly to give a target to a link Zoran put on the Cafe. If this is counter to your intention for the link, Zoran, I can remove the redirect and put in a stub instead.
I added two new important references on global analytic geometry, also due to Poineau. He shows there that the sheaf of analytic functions is coherent. This is an interesting fundamental result.
started derived loop space
technical details to follow
Couldn’t find an existing “latest changes” thread for the quasifibration page (http://ncatlab.org/nlab/show/quasifibration), but just wanted to remark that I put another reference in there, to a nice expository paper by Peter May.
-Jon
I wrote a little piece at general covariance on how to formalize the notion in homotopy type theory. Just for completeness, I also ended up writing a little blurb at the beginning about the genera idea of general covariance.
Created lambda calculus.
I have added pointer to Mike’s discussion of spectral sequences here at “homotopy spectral sequence” and in related entries.
But now looking at this I am unsure what the claim is: has this been formalized in HoTT?
(Clearly a question for Mike! :-)
expanded the entry cofinal functor: formal definition, list of equivalent characterizations and textbook reference.
Just an editorial matter:
noticed that section did not point to space of sections and not to dependent product in the text. So I briefly added a paragraph to this extent.
How would you define the usual jargon “fragment” in logic?
There ought to be a simple formal definition, I suppose, such as “Given a language L and a theory T in that language, then a fragment of T is… “
created topological localization
added to periodic ring spectrum and to periodic cohomology theory a brief paragraph on looping/delooping periodicity on the -modules, with a pointer to this MO discussion
created anti-reduced object, for completeness
Discussion with Mike reminded me that we were lacking an entry reflective subuniverse.
I started a template and cross-linked, but now I am out of battery and time before filling in any content. Will do that tomorrow.
some bare minimum at Chaitin’s incompleteness theorem
This is to flag up two entries that so-far just have titles. They are IulianUdrea and perfectly normal space. These may need watching. The second may be ok, and be a page somone has just started and intends to continue, but the name on the second also occurs as a name on a Mo page with no questions and no answers and may be someone seeing how many wikis etc they can put stuff on! Sorry for being a nasty suspicious b*****, but it looks a bit strange to me.
(N.B., the two entries do not seem to be related.)
at diffeomorphism I started listing theorems and references on statements about when the existence of a homeomorphism implies the existence of a diffeomorphism.
I dug out ancient references for the statement that in everything homeomorphic to an open -ball is also diffeomorphic to it. What would be a more modern, more canonical, more textbook-like reference for this?
And I’d also like to cite a reference for what is maybe obvious, that if that something in is an open subset of equipped with the induced smooth structure of the standard smooth structure, then the statement is also true in that dimension.
In fact, I am looking for nice/explicit/useful diffeomorphisms from the open -ball onto the open -simplex. I can of course fiddle around and cook up something, but I haven’t found anything that would count as nice. But probably some engineer out there working with finite elements or something does have a convenient choice.
there is this new master thesis:
which discusses aspects of weak Tarskian homotopy type universes following the indications that Mike Shulman has been making, for instance at universe (homotopytypetheory). I just got permission to share this and I have now included pointers to the thesis to that entry, to type of types, etc.
Created Vopenka’s principle.
At some point I had made up the extra axiom/terminology saying that an object in a cohesive -topos “exhibits the cohesion” if the shape modality is equivalent to -localization. Now I was talking about that assumption with Mike and noticed that this didn’t have a reflection on the Lab yet.
So now I have added, for the record, the definition here at “cohesive oo-topos” and cross-linked with the existing discussion at “continuum”.
added recent AlgTop mailing list contribution on fibrant replacement of cubical sets to cubical set
started some minimum at Prym-Tyurin variety
Have added the “definition” of a symmetric monoidal -category to the entry.
walt has replied to an old question of Mike at semi-abelian category.
Urs has created page Stanisław Woronowicz on Sep 10. However there is an old page for the same person, with publication version S. L. Woronowicz in Lab, with extensive reference list which was redirecting the full name Stanisław Lech Woronowicz as well as Stanisław L. Woronowicz.
I’ve written a stub on Cole’s theory of spectrum which for the time being consists largely of references and links. Further curation or correction would be appreciated!
added to (infinity,n)-category of spans a pointer to the discussion of -categories of spans in section 10 of
David Mumford has a treasure trove of free material at his website, so I added a link to his page.
I have added several historically important references at space-time.
I created the stub children’s drawing.
I did a bit of editing (of Definition and Examples) at child’s drawing (once known as children’s drawing), to emphasize that a child’s drawing/dessin d’enfant is not simply a hypermap, but (typically) a hypermap seen as the representation of a Belyi function. I was guided by the presentation in Lando & Zvonkin 2004 (this paper by Zvonkin is also helpful), but apologies if I introduced any mistakes since I’m just learning this stuff.
Few references collected as a start of entry spectrum of a graph redirecting also Ihara zeta function, prompted by today’s remarkable paper by Huang and Yau and thereby revived memory of a colloqium talk by Bass in which I enjoyed at University of Wisconsin in late 1990s.
added to group completion a paragraph with minimum pointers to the traditional construction as group completion of topological monoids. Added a corresponding brief paragraph to K-theory of a permutative category (where this had been missing).
What is still missing (on the Lab and maybe generally in the literature) is a really clear statement that this is indeed a model for the -categorical group completion operation which is invoked at K-theory of a symmetric monoidal (infinity,1)-category.
One place where such a derived functor statement is made is Dwyer-Kan 80, remark 9.7 (thanks to Charles Rezk’s MO comment here). I have added pointers to that to the relevant entries, but this ought to be sorted out in more detail.
wrote something at baryogenesis
What mathematicians call the Mellin transform relating a theta function to its (completed) zeta function
is precisely what physicists call the Schwinger parameter-formulation which takes the partition function of the worldline formalism to the zeta-regulated Feynman propagator
I have tried to briefly mention this relation in relevant entries and to cross-link a bit. But more should be done.
I created a stub on Sam Gitler who has recently died. He was very important not only for his contribution to Yang-Mills theory and the Brown-Gitler spectrum, but also for his creation, with Adem of the school of algebraic topology in Mexico. (I have changed all the mentions of Gitler to be ‘active’.)
I have not yet made this change – as a newbie, I want to get an opinion first.
associative unital algebra describes an -algebra , for commutative, as a “ring under ”. From under category, this is just an object in the coslice category : a map , where is another ring. However, I believe that such a map gives an -algebra only if its image is in the center of (for example, Wikipedia). I’m not sure how to fix that. Maybe we should just remove the “under ” item from that first page. Thoughts?