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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 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.
Stub context-free grammar.
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.
brief category:people-entry for hyperlinking references at gauge-Higgs unification and at Higgs field, GUT and elsewhere
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 or of . Is that a global family? I.e. is it closed under quotient groups by normal subgroups?
I made “classification of simple Lie groups” a redirect to this entry, and added a graphics showing the Dynkin diagram correspondence (added that also to Dynkin diagram)
but somebody should really start an entry of that title and do it some justice
started a stub, to satisfy links at Dwyer-Wilkerson space
Mike added two new relevant links to WISC.
I added a section about internal WISC, and changed what was about ’internal WISC’ to ’external WISC in other categories’.
Over at Monster group, I wrote out a description via a group presentation. Of course, it makes no pretense to be illuminating (although it is well-known to experts like Conway; it’s probably in his book with Sloane on the Leech lattice and sphere packings).
Some stuff at Mathieu group, including the fact there are several of them and references to the binary Golay code, of which the largest Mathieu group is the automorphism group.
stub for type II geometry