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added to identity type a mentioning of the alternative definition in terms of inductive types (paths).
added pointer to today’s
Added pointer to today’s
Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Maximal supergravities from higher dimensions [arXiv:2309.07232]
Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Consistent truncation of eleven-dimensional supergravity on [arXiv:2309.07233]
I created a short page for chord diagram, and also added a bit of relevant information to Vassiliev invariant.
stub for Goodwillie calculus
I gave Drinfel’d double an Idea-section.
Also moved a paragraph on module categories from the References to a Properties-section.
Started a bare minimum at cyclotomic spectrum. So far it’s essentially just a pointer to the canonical reference by Blumberg-Mandell. (Thomas Nikolaus and Peter Scholze have a new foundation of the theory in preparation for which notes however are not public yet, also Clark Barwick has something in preparation, for which you may find notes by looking at his website and being clever in deducing hidden URLs, he says.)
For the moment the only fact that I have actually recorded in the entry is a fact that is trivial for anyone familiar with the theory,but which looks interesting from the point of view of the story at Generalized cohomology of M2/M5-branes (schreiber): the global equivariant sphere spectrum for all the cyclic groups (all the A-type finite groups in the ADE classification…) carries canonical cyclotomic structure and as such is the tensor unit among cyclotomic spectra.
Apart from mentioning this, I have added brief cross-links with topological cyclic homology, equivariant sphere spectrum, cyclic group and maybe other entries.
stub for quantum sheaf cohomology
Created solid functor with an SVG graphic. The SVG editor is awesome! Even if it is still a little buggy.
Added to derivator the explanation that Denis-Charles Cisinski had posted to the blog.
Zoran, I have made the material you had here the section "References", as this was mainly pointers to the literature. Please move material that you think you should go into other sections.
Stub, separating from (total) symbol of a differential operator.
wrote something at symbol of a differential operator
brief entry superoperator, just for completeness
brief definition: positive operator
added pointer to the original:
started an entry Planck’s constant with a remark on its meaning from the point of view of geometric quantization (and nothing else, so far).
started some minimum at Bost-Connes system.
Hm, it seems that the statement is that that partition function of the BC-system
is the Riemann zeta function. But by the pertinent analogies the zeta functions are not supposed to equal partition functions, but to be related to them by the transformation
Hm.
am finally giving this its own entry, to be split off (not done yet) from D-brane charge and to be in parallel with K-theory classification of topological phases of matter
added pointer to what seems to be the origin of the notion of density matrices:
John von Neumann, §IV, §V in:
Mathematische Grundlagen der Quantenmechanik, Springer (1932, 1971) [doi:10.1007/978-3-642-96048-2]
Mathematical Foundations of Quantum Mechanics Princeton University Press (1955) [doi:10.1515/9781400889921, Wikipedia entry]
some basic text at hidden variable theory, just so as to satisfy some links…
I have slightly touched the paragraph Syntax and semantics at evaluation map.
And then I added to the entry internal hom a similar Propeties-section internal hom - Evaluation map
a page to record the 2-term relation on horizontal chord diagrams, to go with the entries 4T relation and horizontal weight system
I added to category of elements an argument for why preserves colimits.
added these pointers on classification of topological phases of matter via tensor network states:
C. Wille, O. Buerschaper, Jens Eisert, Fermionic topological quantum states as tensor networks, Phys. Rev. B 95, 245127 (2017) (arXiv:1609.02574)
Andreas Bauer, Jens Eisert, Carolin Wille, Towards a mathematical formalism for classifying phases of matter (arXiv:1903.05413)
The entry Lie algebra extension used to have only a discussion of the fairly exotic topic of classification in nonabelian Lie algebra cohomology. I have now added an Idea-section with some more introductory and more traditional remarks. This could well be expanded much further.
Hi. I found myself :) Thanks for this page. I replaced the links to the recently removed page at Royal Holloway to link to my permanent home page dusko.org. There are in the meantime I think more important publications on arxiv, and the LICS 1998 paper on Calculus in coainductive form with Martin Escardo is cited a lot, but you’ll probably know better whether any of that is really of interest :) – dusko
dusko
started a minimum at Anderson duality just for compleness, see the other thread on dualizing object in a closed category.
I gave the brane scan table a genuine Lab incarnation and included it at Green-Schwarz action functional and at brane.
Somebody named Adam left a comment box a while ago at premonoidal category saying that naturality of the associator requires three naturality squares. I believe that this is true when phrased explicitly in terms of one-variable functors, but the slick approach using the “funny tensor product” allows us to rephrase it as a single natural transformation between functors . I’ve edited the page accordingly. I also added the motivating example (the Kleisli category of a strong monad) and a link to sesquicategory.
There is a comment on the page that “It may be possible to weaken the above make a symmetric monoidal 2-category, in which a monoid object is precisely a premonoidal category”. However, the Power-Robinson paper says that “We remark that is not a 2-functor,” which seems to throw some cold water on the obvious approach to that idea. Was the thought to define a different 2-categorical structure on than the usual one, e.g. using unnatural transformations? It seems that at least one would still have to explicitly require centrality of the coherence isomorphisms.
added pointer to today’s
did some substantial edits on this entry:
gave it more of an Idea-section,
tried to streamline the statement of the lemma
spelled out the proof,
added a discussion explaining how this is about irreps forming a (de-)categorified orthogonal/orthonormal linear basis of the representation ring.
saw activity at simple object and started a tiny section with examples.
Started 12-dimensional supergravity following some discussion with Urs.
added to Lie algebra a brief paragraph general abstract perspective to go along with this MO reply
expanded and polished Kalb-Ramond field. In particular I added more references.
I made a little addition to opposite category, pointing out some amusing nuances regarding the opposite of a -enriched category when is merely braided. This remark could surely be clarified, but I think you’ll get the idea.
(In case you’re wondering why I did this, it’s because I needed a reference for “opposite category” in a blog entry I’m writing.)
Under definition 1 of salamander lemma, I fixed a mistake in the definition of where there was a direct sum of two submodules, where there needed to be a sum (i.e., join) instead.
following public demand, I added to tensor product of chain complexes a detailed elementary discussion of the tensor product of the (normalized) chain interval with itself, and how it gives chains on the cellular square: in Square as tensor product of interval with itself.