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brief category:people-entry for hyperlinking references at stable homotopy theory
I am planning to write a few things about Picard groupoids. For this purpose, I have removed a couple of redirects from Picard 2-group, added a new one which is a bit more precise, and tweaked the beginning of this page slightly. Feel free to edit further; I basically just wished to free up the page Picard groupoid.
some minimum, just so to have a canonical place for linking references jointly from LHC and flavour anomaly
brief note on Whitney extension theorem
Added redirect for missing link at Banach algebra section “2. Examples”.
Anonymous
added to coalgebra for an endofunctor the example of the real line as the terminal coalgebra for some endofunctor on Posets.
There are more such characterizations of the real line, and similar. I can't dig them out right now as I am on a shky connection. But maybe somebody else can. Or I'll do it later.
brief category:people-entry for hyperlinking references at non-abelian T-duality and elsewhere
brief category:people-entry for hyperlinking references on twisted equivariant KR-theory of orbi- orientifolds
brief category:people-entry for hyperlinking references at orientifold, O-plane, RR-field tadpole cancellation and MO5
expanded chain homotopy: added the usual non-commuting diagram, a discussion of chain homotopy equivalence and slightly expanded the description in terms of left homotopy
A long time ago we had a discussion at graph about notions of morphism. I have written an article category of simple graphs which collects some properties of the category under one of those definitions (corresponding better, I think, to graph-theoretic practice).
I just aadded a sentence about Yang-Mills theory to gauge group, but there are some aspects of that article I feel we might want to discuss:
I don’t think that the statement “gauge groups encoded redundancies” of the mathematical description of the physics is correct. One hears this every now and then, and I suppose the idea is the observation that physical observables have to be in the trivial representation of the gauge group, but there is more to the gauge group than that.
Notably Yang-Mills theory is a theory of connections on G-principal bundles. No mathematician would ever say that the group G in a G-principal bundle just encodes a redundancy of our descriptins of that bundle. And the reason is because it is true only locally: the thing is that BG={*g∈G→*} has a single object and hence is connected , but it has higher homotopy groups, and that’s where all the important information encoded by the gauge group sits.
So I would say that instead of being a redundancy of the description, instead the gauge group of Yang-Mills theory enocedes precisely the homotopy type of its moduli space. This is rather important.
A different matter are global gauge symmetries such as those that the DHR-theory deals with.
am starting this for completeness, in the context of a more general entry Dp-D(p+4)-brane bound state. Nothing much here yet
started some bare minimum omn RR-field tadpole cancellation. Currently I am using this just to complement discussion at intersecting D-brane models
am giving this table from the entry RR-field tadpole cancellation its stand-alone entry, so that it may be !include-ed into other relevant entries, such as at intersecting D-brane model
Restructured the manifold entry to avoid duplication with pseudogroup, and moved the section on the tangent bundle to tangent bundle
SC LOL (182.55.198.94) started a page called e, which roughly makes sense.
as promised (to Domenico), a stub for characteristic class
a stubby minimum at maybe monad
(we are talking about it in the other thread, but for completeness I suppose I should start a new thread for it here)
I have given pseudogroup an entry of its own, for the moment just copying there the definition from manifold. This is so as to be able to add references for the concepts, which I did.
added more references to 2-spectral triple (as far as I can see Jürg Fröhlich with his students was the first to try to formalize this to some extent)
Finally started ZFC.
it is long overdue that we create a table listing what appears in the ADE pattern.
In a stolen minute I gave it a start at ADE – table.
stub, just to fill an entry in low dimensional rotation groups – table
stub, just to fill an entry in low dimensional rotation groups – table
I have created a minimum at global family (a suitable family of groups in the sense of global equivariant homotopy theory).
Hm, the set of finite subgroups of SO(3) or of SU(2). Is that a global family? I.e. is it closed under quotient groups by normal subgroups?