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am splitting this off from holographic QCD, since the latter is getting too crowded. Prompted by today’s
added a sentence to the Idea-section at Kan complex
added the pointers to the combinatorial proofs of the fiberwise detection of acyclicity of Kan fibrations, currently discussed on the AlgTop list, to the nLab here.
I moved the definition of promonoidal categories from Day convolution to promonoidal category, and expanded on it a bit.
I have added at HomePage in the section Discussion a new sentence with a new link:
If you do contribute to the nLab, you are strongly encouraged to similarly drop a short note there about what you have done – or maybe just about what you plan to do or even what you would like others to do. See Welcome to the nForum (nlabmeta) for more information.
I had completly forgotton about that page Welcome to the nForum (nlabmeta). I re-doscivered it only after my recent related comment here.
This page has been ‘mucked up’. The table has been destroyed giving just a block of text. I could roll back but thought it better for people to see the mess!
created stub for Barr’s theorem (If a statement in geometric logic is deducible from a geometric theory using classical logic and the axiom of choice, then it is also deducible from it in constructive mathematics.)
I added to walking structure a 2-categorical theorem that implies that usually “the underlying X of the walking X is the initial X”. This fact seems like it should be well-known, but I don’t offhand know a reference for it, can anyone give a pointer?
a stub, for the moment just to ungray a link at exotic meson
starting some minimum, to go with XYZ meson and tetraquark
I made some changes to bivector. While the idea section is correct (and should be strictly adhered to!) but the previous definition is wrong in general! The previous definition is consistent and used in wikipedia but it misses both the direct relation of bivectors, trivectors and general polyvectors to determinants as well as the standard nontrivial usage of bivectors in analytic geometry wher bivectors define equivalence classes of parallelograms and in particular with a point in space given define an affine plane. If we adhere to wikipedia and not to standard treatments in geometry (e.g. M M Postnikov, Analytic geometry) then we miss the nontriviality of the notion of bivector and its meaning which is more precise than that of a general element in the second exterior power.
Bivector in a vector space is not any element in the second exterior power, but a DECOMPOSABLE vector in the second tensor power – in general dimension just such elements in have the intended geometric meaning and define vector 2-subspaces and of course affine 2-subspaces if a point in the 2-subspace is given. It is true that every bivector in 2-d or in 3-d space is decomposable, but in dimension 4 this is already not true. Thus the bivectors form a vector space just in the dimensions up to . Similarly, trivectors form a vector space just in the dimensions up to . In the context of differential graded algebras, polyvector fields are usually taken as arbitrary elements in the exterior powers of vector fields.
I am giving this its own entry, to go alongside hadron supersymmetry, but right now it contains mustly just the commented references from hadrons as KK-modes of 5d Yang-Mills theory – references
brief category:people-entry for hyperlinking references at Skyrmion and D=5 Yang-Mills theory
brief category:people-entry for hyperlinking references at Skyrmion and D=5 Yang-Mills theory
started something. For the moment really just a glorified pointer to Buchert et al. 15 and putting Scharf 13 into perspective