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

• 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

• 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.

• starting something

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• am starting something

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

• 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.

• made some minor cosmetic edits, such as replacing

\bar W G

(which comes out with too short an overline) with

\overline{W} G

• Simply the definition, as found in “Combinatorics of coxeter groups” by Bjorner and Brenti.

Anonymous

• 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”?

• 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:

• some minimum, for completeness of the list at D4

• more hyperlinks (and some whitespace) to the paragraph on maximal tori.

• the statement that smooth actions of compact Lie groups on smooth manifolds are proper

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