Not signed in (Sign In)

A discussion forum about contributions to the nLab wiki and related areas of mathematics, physics, and philosophy.

Want to take part in these discussions? Sign in if you have an account, or apply for one below

2-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories newpage nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes science set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

- Discussion Type
- discussion topicSupersymmetries and their Representations
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

added these pointers:

For analogous discussion see

- Steven Shnider,
*The superconformal algebra in higher dimensions*, Letters in Mathematical Physics November 1988, Volume 16, Issue 4, pp 377-383 (doi:10.1007/BF00402046)

and for review see

- Shiraz Minwalla, Section 4.2 of:
*Restrictions imposed by superconformal invariance on quantum field theories*, Adv. Theor. Math. Phys. 2, 781 (1998) (arXiv:hep-th/9712074, doi:10.4310/ATMP.1998.v2.n4.a4)

- Steven Shnider,

- Discussion Type
- discussion topicsuperconformal symmetry -- table
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 2 days ago

this table used to be hidden at

*supersymmetry*, but it really ought to cross-link its entries. Therefore here its stand-alone version, for !inclusion

- Discussion Type
- discussion topicM5-brane
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active 2 days ago

I have added to

*M5-brane*a fairly detailed discussion of the issue with the fractional quadratic form on differential cohomology for the dual 7d-Chern-Simons theory action (from Witten (1996) with help of Hopkins-Singer (2005)).In the new section

*Conformal blocks and 7d Chern-Simons dual*.

- Discussion Type
- discussion topicAlbert Einstein
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 3 days ago

added this pointer:

Peter Coles,

*Einstein, Eddington, and the 1919 Eclipse*(arxIv:astro-ph/0102462)(on the experimental confirmation of general relativity)

- Discussion Type
- discussion topicSchwinger effect
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicD=5 super Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 3 days ago

added pointer to more references, in particular these on the relation to the D=6 N=(2,0) SCFT via KK-compactification on a circle fiber, hence as worldvolume theory of the D4-brane double dimensional reduction of the M5-brane:

Nathan Seiberg, Sec. 7 of

*Notes on Theories with 16 Supercharges*, Nucl. Phys. Proc. Suppl. 67:158-171, 1998 (arXiv:hep-th/9705117){#Douglas11} Michael Douglas,

*On D=5 super Yang-Mills theory and (2,0) theory*, JHEP 1102:011, 2011 (arXiv:1012.2880)Neil Lambert, Constantinos Papageorgakis, Maximilian Schmidt-Sommerfeld,

*M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills*, JHEP 1101:083, 2011 (arXiv:1012.2882){#Witten11} Edward Witten, Sections 4 and 5 of

*Fivebranes and Knots*(arXiv:1101.3216)Chris Hull, Neil Lambert,

*Emergent Time and the M5-Brane*, JHEP06(2014)016 (arXiv:1403.4532)Andreas Gustavsson,

*Five-dimensional Super-Yang-Mills and its Kaluza-Klein tower*. JHEP01(2019)222 (arXiv:1812.01897)Neil Lambert, Sec. 3.1 and 3.4.3. of

*Lessons from M2’s and Hopes for M5’s*,*Proceedings of the LMS-EPSRC Durham Symposium:**Higher Structures in M-Theory, August 2018*Fortschritte der Physik, 2019 (arXiv:1903.02825, slides pdf)

- Discussion Type
- discussion topicMax Zimet
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicArnav Tripathy
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicRiemannian orbifold
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicsimplicial loop space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

added pointer to

- Danny Stevenson,
*Décalage and Kan’s simplicial loop group functor*, Theory and Applications of Categories, Vol. 26, 2012, No. 28, pp 768-787 (arXiv:1112.0474, tac:26-28)

- Danny Stevenson,

- Discussion Type
- discussion topicsimplicial object
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 4 days ago

added to simplicial object a section on the canonical simplicial enrichment and tensoring of $D^{\Delta^{op}}$ for $D$ having colimits and limits.

- Discussion Type
- discussion topicmodel structure on simplicial groups
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 4 days ago

added pointer to the original statement in

- Daniel Quillen, p. II 3.7 of:
*Axiomatic homotopy theory*in:*Homotopical Algebra*, Lecture Notes in Mathematics 43, Springer 1967(doi:10.1007/BFb0097438)

- Daniel Quillen, p. II 3.7 of:

- Discussion Type
- discussion topicderivator
- Category Latest Changes
- Started by Urs
- Comments 81
- Last comment by Mike Shulman
- Last Active 4 days ago

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 topicinhomogeneous cosmology
- Category Latest Changes
- Started by Urs
- Comments 28
- Last comment by Urs
- Last Active 4 days ago

started something. For the moment really just a glorified pointer to Buchert et al. 15 and putting Scharf 13 into perspective

- Discussion Type
- discussion topicBorel model structure
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicBN-pair
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topictensor triangulated category
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 5 days ago

In articles by Balmer I see “tensor monoidal category” to be explained as a triangulated category equipped with a symmetric monoidal structure such that tensor product with any object “is an exact functor”, but I don’t see where he is specific about what “exact functor” is meant to mean. Maybe I am just not looking in the right article.

Clearly one wants it to mean “preserving exact triangles” in some evident sense. One place where this is made precise is in def. A.2.1 (p.106) of Hovey-Palmieri-Strickland’s “Axiomatic stable homotopy theory” (pdf).

However, these authors do not use the terminology “tensor triangulated” but say “symmetric monoidal compatible with the triangulation”. On the other hand, Balmer cites them as a reference for “tensor triangulated categories” (e.g. page 2 of his “The spectrum of prime ideals in tensor triangulated categories” ).

My question is: may I assume that “tensor triangulated category” is used synonymously with Hovey-Palmieri-Strickland’s “symmetric monoidal comaptible with the triangulation”?

- Discussion Type
- discussion topicDrinfeld center
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicspectrum of a tensor triangulated category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 5 days ago

added pointer to

Paul Balmer,

*The spectrum of prime ideals in tensor triangulated categories*. J. Reine Angew. Math., 588:149–168, 2005 (arXiv:math/0409360)Paul Balmer,

*Spectra, spectra, spectra—tensor triangular spectra versus Zariski spectra of endomorphism rings*, Algebr. Geom. Topol., 10(3):1521–1563, 2010 (pdf)

(which have been listed at

*Paul Balmer*all along, but were missing here, strangely)and to the recent:

- Kent B. Vashaw,
*Balmer spectra and Drinfeld centers*(arXiv:2010.11287)

- Discussion Type
- discussion topicmodel structure on equivariant dgc-algebras
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 5 days ago

starting something, on

- Laura Scull,
*A model category structure for equivariant algebraic models*, Transactions of the American Mathematical Society 360 (5), 2505-2525, 2008 (doi:10.1090/S0002-9947-07-04421-2)

- Laura Scull,

- Discussion Type
- discussion topicKlein four-group
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topiccompact Lie group
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicorbit category
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 6 days ago

added to

*orbit category*a remark on what the name refers to (since I saw sonebody wondering about that)

- Discussion Type
- discussion topicMonsky-Washnitzer cohomology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

- Discussion Type
- discussion topicn-truncated object of an (infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Hurkyl
- Last Active 6 days ago

- Discussion Type
- discussion topicJaap Kalkman
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

brief

`category: people`

-entry for hyperlinking references at*equivariant de Rham cohomology*

- Discussion Type
- discussion topicHiggs field
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Urs
- Last Active 7 days ago

added a brief historical comment to

*Higgs field*and added the historical references

- Discussion Type
- discussion topicFinRel
- Category Latest Changes
- Started by John Baez
- Comments 5
- Last comment by DavidRoberts
- Last Active 7 days ago

- Discussion Type
- discussion topicbimonoid
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by John Baez
- Last Active 7 days ago

Added to bimonoid the fact that the category of modules over a bimonoid is monoidal.

- Discussion Type
- discussion topicuniversal coefficient theorem
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 7 days ago

started universal coefficient theorem