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- Discussion Type
- discussion topicquantum decoherence
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Sep 15th 2023

added pointer to today’s

- Chris Nagele, Oliver Janssen, Matthew Kleban,
*Decoherence: A Numerical Study*(arXiv:2010.04803)

- Chris Nagele, Oliver Janssen, Matthew Kleban,

- Discussion Type
- discussion topicGianluca Inverso
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 15th 2023

- Discussion Type
- discussion topicFranz Ciceri
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 15th 2023

- Discussion Type
- discussion topicD=2 supergravity
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 15th 2023

Added pointer to today’s

Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt,

*Maximal $D=2$ supergravities from higher dimensions*[arXiv:2309.07232]Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt,

*Consistent truncation of eleven-dimensional supergravity on $S^8 \times S^1$*[arXiv:2309.07233]

- Discussion Type
- discussion topicchord diagram
- Category Latest Changes
- Started by Noam_Zeilberger
- Comments 13
- Last comment by Urs
- Last Active Sep 15th 2023

I created a short page for chord diagram, and also added a bit of relevant information to Vassiliev invariant.

- Discussion Type
- discussion topicGoodwillie calculus
- Category Latest Changes
- Started by Urs
- Comments 44
- Last comment by nonemenon
- Last Active Sep 14th 2023

stub for Goodwillie calculus

- Discussion Type
- discussion topicDrinfel'd double
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by nLab edit announcer
- Last Active Sep 14th 2023

I gave

*Drinfel’d double*an Idea-section.Also moved a paragraph on module categories from the References to a Properties-section.

- Discussion Type
- discussion topiccyclotomic spectrum
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by Urs
- Last Active Sep 14th 2023

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.

- Discussion Type
- discussion topicquantum cohomology ring
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Sep 14th 2023

stub for quantum sheaf cohomology

- Discussion Type
- discussion topicsolid functor
- Category Latest Changes
- Started by Mike Shulman
- Comments 8
- Last comment by varkor
- Last Active Sep 13th 2023

Created solid functor with an SVG graphic. The SVG editor is awesome! Even if it is still a little buggy.

- Discussion Type
- discussion topicstructural ZFC
- Category Latest Changes
- Started by nLab edit announcer
- Comments 6
- Last comment by nLab edit announcer
- Last Active Sep 13th 2023

- Discussion Type
- discussion topictopological T-duality
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Sep 12th 2023

- Discussion Type
- discussion topicderivator
- Category Latest Changes
- Started by Urs
- Comments 126
- Last comment by Urs
- Last Active Sep 12th 2023

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.

- Discussion Type
- discussion topicSumeet Khatri
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 12th 2023

- Discussion Type
- discussion topicMark M. Wilde
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 12th 2023

- Discussion Type
- discussion topicprincipal symbol
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Sep 12th 2023

Stub, separating from (total) symbol of a differential operator.

- Discussion Type
- discussion topicsymbol of a differential operator
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by zskoda
- Last Active Sep 12th 2023

wrote something at

*symbol of a differential operator*

- Discussion Type
- discussion topicsuperoperator
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 12th 2023

brief entry

*superoperator*, just for completeness

- Discussion Type
- discussion topicpositive operator
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 12th 2023

brief definition:

*positive operator*

- Discussion Type
- discussion topicbra-ket
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 12th 2023

added pointer to the original:

- Paul A. M. Dirac,
*A new notation for quantum mechanics*, Mathematical Proceedings of the Cambridge Philosophical Society**35**3 (1939) 416-418 [doi:10.1017/S0305004100021162, pdf]

- Paul A. M. Dirac,

- Discussion Type
- discussion topicPlanck's constant
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Sep 12th 2023

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).

- Discussion Type
- discussion topicBost-Connes system
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Tom Mainiero
- Last Active Sep 11th 2023

started some minimum at

*Bost-Connes system*.Hm, it seems that the statement is that that partition function of the BC-system

$\beta \mapsto Tr(\exp(- \beta H_{BostConnes}))$is the Riemann zeta function. But by the pertinent analogies the zeta functions are not supposed to

$s \mapsto \int_0^\infty \beta^{s-1} \left(Tr(\exp(- \beta H)) -1\right)\; d \beta \,.$*equal*partition functions, but to be related to them by the transformationHm.

- Discussion Type
- discussion topicD-brane charge quantization in K-theory
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Sep 11th 2023

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*

- Discussion Type
- discussion topicinfinitesimal braid relation
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by zskoda
- Last Active Sep 11th 2023

- Discussion Type
- discussion topicdensity matrix
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2023

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]

- Discussion Type
- discussion topichidden variable theory
- Category Latest Changes
- Started by Urs
- Comments 101
- Last comment by Urs
- Last Active Sep 11th 2023

some basic text at

*hidden variable theory*, just so as to satisfy some links…

- Discussion Type
- discussion topicPaul H. Frampton
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2023

- Discussion Type
- discussion topicfunctional programming
- Category Latest Changes
- Started by AlexisHazell
- Comments 9
- Last comment by Urs
- Last Active Sep 10th 2023

- Discussion Type
- discussion topicevaluation map
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 10th 2023

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*

- Discussion Type
- discussion topicTomas Petricek
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 10th 2023

- Discussion Type
- discussion topicAlan Mycroft
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 10th 2023

- Discussion Type
- discussion topicline bundle
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Sep 10th 2023

- Discussion Type
- discussion topic2T relation
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 9th 2023

a page to record the 2-term relation on horizontal chord diagrams, to go with the entries

*4T relation*and*horizontal weight system*

- Discussion Type
- discussion topicYong-Baek Kim
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 8th 2023

- Discussion Type
- discussion topicMatthew Fisher
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 8th 2023

- Discussion Type
- discussion topicLukasz Fidkowski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 8th 2023

- Discussion Type
- discussion topiccategory of elements
- Category Latest Changes
- Started by Mike Shulman
- Comments 7
- Last comment by nLab edit announcer
- Last Active Sep 8th 2023

I added to category of elements an argument for why $El$ preserves colimits.

- Discussion Type
- discussion topictopological phase of matter
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active Sep 8th 2023

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)

- Discussion Type
- discussion topicLie algebra extension
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by perezl.alonso
- Last Active Sep 8th 2023

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.

- Discussion Type
- discussion topicCenter for Quantum and Topological Systems
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Sep 8th 2023

- Discussion Type
- discussion topicDuško Pavlović
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Sep 8th 2023

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

- Discussion Type
- discussion topicAnderson duality
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 8th 2023

started a minimum at

*Anderson duality*just for compleness, see the other thread on*dualizing object in a closed category*.

- Discussion Type
- discussion topicbrane scan
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by perezl.alonso
- Last Active Sep 8th 2023

I gave the brane scan table a genuine $n$Lab incarnation and included it at

*Green-Schwarz action functional*and at*brane*.

- Discussion Type
- discussion topicpremonoidal category
- Category Latest Changes
- Started by Mike Shulman
- Comments 30
- Last comment by Matt Earnshaw
- Last Active Sep 8th 2023

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 $C\otimes C\otimes C\to C$. 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 $(Cat,\otimes)$ 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 $(C \otimes -) : Cat \to Cat$ 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 $Cat$ 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.

- Discussion Type
- discussion topicchiral anomaly
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 8th 2023

added pointer to today’s

- Valentin Benedetti, Horacio Casini, Javier M. Magan,
*ABJ anomaly as a $U(1)$ symmetry and Noether’s theorem*[arXiv:2309.03264]

- Valentin Benedetti, Horacio Casini, Javier M. Magan,

- Discussion Type
- discussion topicSchur's lemma
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by John Baez
- Last Active Sep 7th 2023

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.

- Discussion Type
- discussion topicsimple object
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by John Baez
- Last Active Sep 7th 2023

saw activity at simple object and started a tiny section with examples.

- Discussion Type
- discussion topicD=12 supergravity
- Category Latest Changes
- Started by David_Corfield
- Comments 23
- Last comment by perezl.alonso
- Last Active Sep 7th 2023

Started 12-dimensional supergravity following some discussion with Urs.

- Discussion Type
- discussion topictopological phases of matter via K-theory -- references
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Emilio V.
- Last Active Sep 7th 2023

- Discussion Type
- discussion topicLie algebra
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Sep 7th 2023

added to

*Lie algebra*a brief paragraph*general abstract perspective*to go along with this MO reply

- Discussion Type
- discussion topicKalb-Ramond field
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Sep 7th 2023

expanded and polished Kalb-Ramond field. In particular I added more references.

- Discussion Type
- discussion topicopposite category
- Category Latest Changes
- Started by John Baez
- Comments 12
- Last comment by nonemenon
- Last Active Sep 7th 2023

I made a little addition to opposite category, pointing out some amusing nuances regarding the opposite of a $V$-enriched category when $V$ 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.)

- Discussion Type
- discussion topicsalamander lemma
- Category Latest Changes
- Started by Todd_Trimble
- Comments 41
- Last comment by DavidRoberts
- Last Active Sep 7th 2023

Under definition 1 of salamander lemma, I fixed a mistake in the definition of $A_\Box$ where there was a direct sum of two submodules, where there needed to be a sum (i.e., join) instead.

- Discussion Type
- discussion topictensor product of chain complexes
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by nLab edit announcer
- Last Active Sep 7th 2023

following public demand, I added to

*tensor product of chain complexes*a detailed elementary discussion of the tensor product $I_\bullet \otimes I_\bullet$ 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*.

- Discussion Type
- discussion topicCarlo Angiuli
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by Urs
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicsynthetic Tait computability
- Category Latest Changes
- Started by David_Corfield
- Comments 7
- Last comment by jonsterling
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicAllan L. Edelson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicWedderburn-Artin theorem
- Category Latest Changes
- Started by John Baez
- Comments 5
- Last comment by John Baez
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicreal vector bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicmodule object
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Sep 6th 2023

expanded the Idea-section and added a reference:

- Francis Borceux, George Janelidze, Gregory Maxwell Kelly, p. 8 of:
*Internal object actions*, Commentationes Mathematicae Universitatis Carolinae (2005) Volume: 46, Issue: 2, page 235-255 (dml:249553)

- Francis Borceux, George Janelidze, Gregory Maxwell Kelly, p. 8 of: