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added to Noether theorem a brief paragraph on the symplectic/Hamiltonian Noether theorem
(I’m currently reading through Keller’s book Differential Calculus in Locally Convex Spaces.)
created product law, since I wanted to be able to link to it…
Created unintentional type theory.
created super Poincare Lie algebra
linked to it from super Euclidean group and from supergravity
stub for Green-Schwarz action functional
I gave the brane scan table a genuine nLab incarnation and included it at Green-Schwarz action functional and at brane.
created an entry type II supergravity Lie 2-algebra.
created differential equation just to link to Lawvere's two articles on that.
Peering through the Lawverian prose, say on page 10 of Toposes of laws of motion I seem to see the shadow of a theory of integration in smooth toposes.
The extension along the inclusion of an infinitesimal object into another object considered there is of the same general nature as the extensins along the inclusion of infnitesimal into all paths that I consider at integration of oo-Lie algebroid valued differential forms.
I mean, no big deal, just something I noticed.
started index theory - contents (somewhat optimistically, for the moment)
added to KK-theory brief remark and reference to relation to stable ∞-categories / triangulated categories
wanted to record Borel’s theorem on Taylor series expansion, so created stubs for power series and Taylor series
Created the page unbounded topos, and some links at topos and bounded geometric morphism.
I’m interested in the generalisation of the construction of the unbounded topos Gl(F) to the general case of an inaccessible comonad G on a bounded topos (which wlog we might as well take to be Set EDIT: NO, LET’S NOT). In essence, why is it unbounded? Also, what nice properties can we claim of the category of coalgebras for G, given information about G.
Note also, the paper HOW LARGE ARE LEFT EXACT FUNCTORS? in TAC in 2001 seems to claim something a little stronger than Johnstone does in the Elephant, and recounted at topos, namely that the existence of lex endofunctors of set is independent of ZFC (they say something more general, but it covers this case). This is mostly a note to myself, but if others feel like looking, that would be good too.
New stubs tropical geometry and tropical semiring (with rig version included). Note the new book by Gross.
There is discussion about material and structural set theories at set theory, spilt over from the Café.
I gave index an Idea-section.
In the course of this I created some stubby auxiliary entries, such as (in rapidly increasing order of stubbieness)
Mishchenko-Fomenko index theorem
Created sampling theory, for the moment just recording some references of my interest.
We should also have Zak transform soon.
added to inter-universal Teichmüller theory a pointer to the recent note
(Though after reading I am not sure if that note helps so much.)
Someone has made a change to the page on Aleksandr Aleksandrov, but there are some characters in the Cyrillic form of his name that are not coming out. Does anyone know how to fix this?
You may have seen in “Recently revised” that I had edited 11-dimensional supergravity in the last days. I wanted to start a section there on the details of the action functional. But after adding some formulas, I ran out of time and just left an “under construction”-warning.
The reason I ran out of time is that I had to first write related things with higher priority into an article we are currently preparing:
Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory.
Later when the dust has settled and I have more leisure, I’ll try to take care of the nLab’s 11d sugra article again.
started Fierz identity to collect some references. Am still searching for the good reference for the general case…
added to hypercomplete (infinity,1)-topos a comment on how classical topos theory models these
(motivated from our discussion here)
added to Cachy real number a pointer to
added to (infinity,n)-category of spans a pointer to the discussion of (∞,2)-categories of spans in section 10 of
made Ben Webster’s recent observation the Idea-section at Hall algebra (see the link given there)
I worked on brushing up (infinity,1)-category a little
mostly I added in a section on homotopical categories, using some paragraphs from Andre Joyal's message to the CatTheory mailing list.
in this context I also rearranged the order of the subsections
I removed in the introduction the link to the page "Why (oo,1)-categories" and instead expanded the Idea section a bit.
added a paragraph to the beginning of the subsection on model categories
added the new Dugger/Spivak references on the relation between quasi-cats and SSet-cats (added that also to quasi-category and to relation between quasi-categories and simplicial categories)
wrote something at cosmic string and by copy-and-pasting-and-changing-the-degrees added something similar to domain wall and monopole. Needs a bit more polishing, maybe.
I am really working on writing out an abstract re-formulation of this classical theory in terms of extended TQFT with defects, but not done with that yet (and will probably be interrupted again before finishing it).
I have started adding references to string field theory , in particular those by Jim Stasheff et al. on the role of L-infinity algebra and A-infinity algebra. Maybe I find time later to add more details.
am in the process of adding some notes on how the D=5 super Yang-Mills theory on the worldvolume of the D4-brane is the double dimensional reduction of the 6d (2,0)-superconformal QFT in the M5-brane.
started a stubby double dimensional reduction in this context and added some first further pointers and references to M5-brane, to D=5 super Yang-Mills theory and maybe elsewhere.
But this still needs more details to be satisfactory, clearly.
Added pointers to
to relevant entries, such as Dijkgraaf-Witten theory and Topological Quantum Field Theories from Compact Lie Groups.