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• felt like adding a handful of basic properties to epimorphism

• considerably expanded the Idea-section

• a table to collect the various cases of transverse geometries to KK-monopoles, to be !include-ded into the relevant entries

• just for completeness

• just for completeness

• just for completeness

• I’ll be working a bit on supersymmetry.

Zoran, you had once left two query boxes there with complaints. The second one is after this bit of the original entry (this will change any minute now)

The theory of supergravity is, as a classical field theory, an action functional on functions on a supermanifold $X$ which is invariant under the super-diffeomorphism group of $X$.

where you say

Zoran: action functional is on paths, even paths in infinitedimensional space, but not on point-functions.

I think you got something mixed up here. If $X$ is spacetime, a field on $X$ is the “path” that you want to see. The statement as given is correct, but I’ll try to expand on it.

The second complaint is after where the original entry said

many models that suggest that the familiar symmetry of various action functionals should be enhanced to a supersymmetry in order to more properly describe fundamental physics.

You wrote:

This is doubtful and speculative. There are many models which have supersymmetry which is useful in their theoretical analysis, but the same models can be treated in formalisms not knowing about supersymmetry. Wheather the fundamental physics needs a model which has nontrivial supersymmetry is a speculative statement, and I disagree with equating theoretical physics with one direction in “fundamental physics”. I do not understand how can a model suggest supersymmetry; it is rather experimental evidence or problems with nonsupersymmetric models. Also one should distinguish the supersymmetry at the level of Lagrangean and the supersymmetry which holds only for each solution of the equation of motion.

I’ll rephrase the original statement to something less optimistic, but i do think that supersymmetry is suggsted more by looking at the formal nature of models than by lookin at the nature of nature. If you have a gauge theory for some Lie algebra (gravity, Poincaré Lie algebra) and the super extension of the Lie algebra has an interesting classification theory (the super Poincar´ algebra) then it is more th formalist in us who tends to feel compelled to investigate this than the phenomenologist. Supersymmetry is studied so much because it looks compelling on paper. Not because we have compelling phenomenological evidence. On the contrary.

So, if you don’t mind, I will remove both your query boxes and slightly polish the entry. Let’s have any further discussion here.

• 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”?