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added pointer to the original article:
am splitting off this entry from exotic smooth strcuture, in order to facilitate linking to specifically the case of exotic 7-sphere.
Accordingly, so far the bulk of the entry is just copied over from the corresponding section at exotic smooth structure,
But I also added a new paragraph,
and that is what motivated me to split this off. Namely it occured to me that from the point of view of M-theory on 8-manifolds, Milnor’s classical construction of exotic smooth 7-spheres as boundaries of 8-manifolds is very particularly the construction of near horizon limits of black M2-brane spacetimes in the context of M-theory on 8-manifolds.
This must be known in the literature, and I’d like to collect what is known about it. So far I found a brief comment in this direction, in section 3.2 of
Will be adding more as I find more.
added to KK-theory brief remark and reference to relation to stable -categories / triangulated categories
Spurred by an MO discussion, I added the observation that coproduct inclusions are monic in a distributive category.
Sum types are distributive coproducts, not just coproducts. I’ll make a page for distributive coproduct next.
Unfortunately, there are two entries on the same topic, both created by Urs: quantum Hall effect (redirecting also fractional quantum Hall effect what should eventually split off) with some substance, and the microstub quantum hall effect. I would like to create quantum spin Hall effect and I think I should rename/reclaim the stub quantum hall effect for this. Do others agree ? Urs ?
As the action is now delayed I record here the reference which I wanted to put there
Somewhat surprisingly, the authors and roughly this work of them are mentioned (though not in the list of references) in a paper in algebraic geometry
which considers the mirror symmetry and topological states of matters (topological insulators in particular) as main applications.
a bare list of references, to be !include-ed into the References-section of relevant entries (such as at braid group representation and at semi-metal).
Had originally compiled this list already last April (for this MO reply) but back then the nLab couldnt be edited
started universal exceptionalism
related discussion is taking place on g+ here
Asked a question at natural transformation.
the term “pre-spectrum” used to re-direct to spectrum and was explained a little more at sequential spectrum. Am giving the term its own page now, for better clarification, prompted by the discussion in another thread (here)
added to van Kampen theorem a clean statement for the group-version
I have touched H-space, slightly expanded here and there and slightly reorganized it.
This is a bare list of references, to be !include-ed into the References-lists of relevant entries (such as at anyon, topological order, fusion category, unitary fusion category, modular tensor category).
There is a question which I am after here:
This seems to be CMT folklore, as all authors state it without argument or reference.
Who is really the originator of the claim that anyonic topological order is characterized by certain unitary braided fusions categories/MTCs?
Is it Kitaev 06 (which argues via a concrete model, in Section 8 and appendix E)?
At equivalence of categories I added a simple example of a non-adjoint equivalence. Maybe it belongs in the page adjoint equivalence instead?
Asked a question at functor.
I added more details in essentially surjective functor. Please check for details (Mike?).
On the page hom-functor, it says
There is also a contravariant hom-functor
where is the opposite category to , which sends any object to the hom-set .
If you write it like this, should you really call it “contravariant”? When you write , I thought you should call it just “functor” or “covariant”. By saying it is contravariant AND writing , it seems like double counting.
I hope to add some illustrations to these pages. It is a shame there are not more illustrations on the nLab since nStuff is so amenable to nice pictures.
Todd,
you added to Yoneda lemma the sentence
In brief, the principle is that the identity morphism is the universal generalized element of . This simple principle is surprisingly pervasive throughout category theory.
Maybe it would be good to expand on that. One might think that the universal property of a genralized element is that every other one factors through it uniquely. That this is true for the generalized element is a tautological statement that does not need or imply the Yoneda lemma, it seems.
added to complete Segal space a discussion of what an ordinary category looks like when regarded as a complete Segal space.
(This is meant to be pedagogical, therefore the recollection of all the basics at the beginning.)
brief category:people-entry for fixing the long requested links at structured cospan
This is my first (substantial) contribution to the nLab, so forgive my likely ineptitude. This wants to be a initial stub, everything is basically scraped from the reference and this post: https://golem.ph.utexas.edu/category/2019/07/structured_cospans.html Clearly a lot of material can be added, included a better definition and clearer examples. It’s also quite necessary to make a page for decorated cospans. I might start it myself later this month.
mattecapu
stub for modular functor
conformal block and Vassily Gorbounov. Update at Imma Galvez.
Created factorization system in a 2-category.