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I created a few stub pages recently: a couple on Saturday for vertex coloring and bipartite graph (thanks to Thomas Holder for a correction and the references), and today the stubbiest of stubs for virtual knot theory.
New stub trigonometry.
Stub for free probability to record some references.
I have added to Kan extension in the section on the pointwise coend formula some elementary illustrative discussion of the case of left Kan extension of presheaves, that some readers might benefit from at this point, see this example.
Someone (at Waldhausen category changed axiom C3) as it was incorrect. The new version still looked wrong, and I have changed it further. (Could someone check that I have got it right now!)
I don’t like the name of the page complete topological space; it seems to suggest that a property of “completeness” can be defined for topological spaces, when in fact one needs additional structure on a topological space (like a metric, a uniformity, or at least a Cauchy structure) in order to say what “complete” means. Since the notion of Cauchy space seems to be the maximum generality in which the notion applies, how about renaming the page to “complete Cauchy space”?
I have been adding some material to Cocomm Coalg. I’m not sure where I first read that this category is extensive, and hope that a relatively painless proof of that can be produced.
It's really the reflection of topological spaces within a larger category, but usually people think of it as underlying: underlying topological space.
have created topos of algebras over a monad
A bit of trivial algebra at trivial subalgebra.
I wrote a constructive definition of simple group, which brought up other issues, so I wrote antisubalgebra and strongly extensional function.
Apparently, the page mathematicscontents, despite being included in a number of other pages, has not existed since shortly after it was spammed slightly more than a year ago. So before blanking a spam page, make sure that it has no history! I have restored it now (although it took a little bit to figure out what it had been called, since it doesn't follow the standard naming format for included contents).
I added a hatnote to syntactic category remarking on an alternative usage of the phrase.
Did some cleaning up and adding to regular category and coherent category, and asked a terminological question at the latter.
I have expanded the text in the entry on Eric Sharpe a little, and added a list of publications. The recent one
reviews and expands on aspects of higher groups/stacks/gerbes in QFT and string theory in a style that ought to appeal to people with physics background.
I came across a non-standard definition of “regular monomorphism” in Cassidy/Hébert/Kelly’s “Reflective subcategories, localizations and factorizations systems.” and added a note to the nlab page. They define a regular mono to be a joint equalizer of an arbitrary family of parallel pairs. This is more general than the usual definition, and forces the class of regular monos to be closed under arbitrary intersections.
I think that in a well powered category with small products the definition should coincide with the usual one, and in coregular categories both should coincide with “strong mono”.
Any comments? Does this definition of regular mono appear anywhere else? Or is there maybe an alternative term for it?
Wrote superextensive site, with a purported proof that sheafification for the single covers does preserve extensive-sheaves in that case.
Have started some minimum at calibration.
Zoran just wrote Hurewicz fibration.
have started a category:reference entry on
and have added pointers to it from relevant entries
I added redirets Atiyah sequence, Atiyah class, Atiyah algebroid to Atiyah Lie algebroid. Maybe we want to have Lie algebroid aspect (concentrating on bracket) and the cohomological/derived category aspect (cohomology class of the exact sequence of modules) separate in fuiture, but now the material is still too small. I added a number of interesting references and a sentence on the class.
created celestial sphere
added a few items to the References section at GUT, both on theoretical background as well as on fits to the latest experimental data. According to these, the -model seems to be well alive, susy or not.
I have created a new entry
meant as a disambiguation page for the various different kinds of definitions that exists. Presently it points to the entries
that already provide dedicated discussion of special defintiions. In addtion it lists references that have further proposals for defintion which don’t at the moment however have dedicated Lab pages associated with them.
Wrote cumulative hierarchy, and edited some at ZFC (idea section, reference, related articles).
started stub for higher parallel transport (but no definition yet, just examples and pointers)
I just noticed we miss an entry n-vector space. I’d like to start it, but I only have a very vague idea, recursively implementing the notion of Baez-Crans 2-vector space. something like: an -vector space is an -category of modules over a -Vect enriched symmetric monoidal -category.
how far is this from the correct notion?
I was going to add a stub page on Roland Schwänzl, to avoid grey links, and linking to the Wikipedia page, but looking at that I am very confused (and my German is too rusty!) That page seems to be about two people or did Roland Schwänzl actually do things on UNIX etc as well as working with Vogt? My search did not even give me the genealogy page for him, (although I now have found it).. Can anyone help?
The nLab presently gives me an application error when trying to open anything, so I’ll record some things here.
The following needs to be added to the References-section of the entry M-theory super Lie algebra:
The M-theory super Lie algebra as first considered in
Jan-Willem van Holten, Antoine Van Proeyen, supersymmetry algebras in J.Phys. A15, 3763 (1982).
Paul Townsend, p-Brane Democracy (arXiv:hep-th/9507048)
Discussion of its formulation in terms of octonions (see also at division algebra and supersymmetry) includes
- A. Anastasiou, L. Borsten, Michael Duff, L. J. Hughes, S. Nagy, An octonionic formulation of the M-theory algebra (arXiv:1402.4649)
I fixed a link that was not working. (The brackets were interfering with the link address.) see here
I created Hoàng Xuân Sính as a result of recent G+ discussion, and David Eppstein creating an English Wikipedia page for her. There is now a link to that page at 2-group and a(n updated) link to her thesis.
for those who check the logs and are wondering: I went through a fairly long list of category:people-entries on people based in and around London, updating affiliation links, references and related Lab entries.
discovered that we already had a stub on Weyl quantization. Cross-linked a bit and added the following reference on Weyl quantization of Chern-Simons theory (also to quantization of 3d Chern-Simons theory):
Jørgen Andersen, Deformation quantization and geometric quantization of abelian moduli spaces, Commun. Math. Phys., 255 (2005), 727–745
Razvan Gelca, Alejandro Uribe, The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on the torus are the same, Commun.Math.Phys. 233 (2003) 493-512 (arXiv:math-ph/0201059)
Razvan Gelca, Alejandro Uribe, From classical theta functions to topological quantum field theory (arXiv:1006.3252, slides pdf)
Razvan Gelca, Alejandro Uribe, Quantum mechanics and non-abelian theta functions for the gauge group (arXiv:1007.2010)
I have added a new link to the page on Grothendieck. There is a good new article on a CNRS site.
given the concept of Heisenberg Lie n-algebra, there is an evident definition of Weyl n-algebra: its universal enveloping E-n algebra.
I noted that down for reference at Weyl n-algebra. In the process I noticed that Markarian proposed a different definition just a few months back
Just some obvious stuff at maximal partial function to satisfy some links.
started a stub for moduli space of Calabi-Yau spaces. Nothing really there yet, except some references and some cross-links.
I tried to start an entry theta function, but it’s hard to tell for me if anything of it has been saved. The Lab is too busy doing something else than serving pages.
I have added the statement of lemmas 4.1, 4.2 of Menni-Lawvere to cohesive topos here and to points-to-pieces transform here.
I am starting a table of contents theta functions - contents and am including it as a “floating table of contents” into relevant entries
The entry entitled (x, y) ⊙ (u, v) = (xu + 2yv, xv + yu) has been started. Is it Spam? or does that definition mean something useful to the nPOV.
made explicit in the Idea section of functional equation the statement that the functional equation of a zeta function is the incarnation under Mellin transform of the automorphy of the automorphic form that it comes from
gave automorphic L-function a minimum of an Idea-section, presently it reads as follows:
An automorphic L-function is an L-function built from an automorphic representation , in nonabelian generalization of how a Dirichlet L-function is associated to a Dirichlet character (which is an automorphic form on the (abelian) idele group).
In analogy to how Artin reciprocity implies that to every 1-dimensional Galois representation there is a Dirichlet character such that the Artin L-function equals the Dirichlet L-function , so the conjectured Langlands correspondence says that to every -dimensional Galois representation there is an automorphic representation such that the automorphic L-function equals the Artin L-function .
stub for holomorphic block, for the moment just to record two references
gave prequantum line bundle a little entry of its own
Wrote Engeler’s lemma, something I hadn’t heard of until recently.
I added a few comments to Hilbert basis theorem about related work by Gordon and Noether (chronologically, on either side of Hilbert’s work).
I created the article left-determined model category.
I had begun adding to prime ideal theorem (en route adding to compactness theorem), but have decided to stop midstream because it looks as though much more general results are known, which I’d need to read up on it before writing further.
One thing I’ll mention now is that the surmise (due to Toby?) that UF is equivalent to the prime ideal theorem for rigs seems to be known and subsumed under these general results. Banaschewski’s name comes up as one having a key lattice-theoretic insight into this topic: “Every nontrivial distributive complete lattice with a compact top element contains a prime element.”
The entry finite field was looking a little sad, so I added to it.
Created splitting field.
Do we have a page about natural transformations between -categories? I wanted to add a link to this paper (working today on catching up with the arXiv…) but I couldn’t find where to put it.
New entry binormal topological space.
am starting power operation, but nothing there yet except references
We have a bit of a mess of closely related entries related to étale homotopy groups which existed more or less in parallel without seeming to know much of each other. I have tried to do some minimum of cross-linking and cleaning up, but this needs more attention.
There is more even, there is Grothendieck’s Galois theory and what not. (Maybe we need to wait until somebody gives a course on this and uses the occasion to clean it all up and harmonize it.)
Created exponent of a group.
I added more material to unique factorization domain.
I’ve slowly been trying to improve the article topological map since this thread. I just added a small note on embedded graphs versus abstract graphs, motivated by Bruce Bartlett’s interesting recent post at the n-café.
I created a stub for falling factorial, mainly to record the simple fact I learned yesterday that it counts the number of injections between two finite sets.