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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• Included the more general definition of Cartan subalgebra from Nathan Jacobson’s book.

• brief category:people-entry for hyperlinking references

• stub

• stub for confinement, but nothing much there yet. Just wanted to record the last references there somewhere.

• Created categorical model of dependent types, describing the various different ways to strictify category theory to match type theory and their interrelatedness. I wasn’t sure what to name this page — or even whether it should be part of some other page — but I like having all these closely related structures described in the same place.

• Added the adjective grouplike to A_infty space as else I just get a monoid object instead of a group object.

Anonymous

• Corrected the definition.

• made some minor cosmetic edits, such as replacing

  \bar W G


(which comes out with too short an overline) with

  \overline{W} G

• for completeness, I have added pointer to

for proof of the Hausdorff property of CW complexes

• Redirect: loop functor.

• added statement of and references to the weak equivalence with the Fulton-MacPherson operad (here)

• Max New: at (129.10.9.38) has put a query on the generalized universal bundle entry. It says:

I don’t understand the above diagram, what is the point $* \to X$ in question? and how does this relate to the universal bundle? In particular, there is a sequence below that has a map from $\Omega_{pt} \to \mathbf{E}_{pt}$ but I don’t see how to construct that from the above.

So I think this is a typo, but I don’t know enough to correct it.

• Add Kanamori reference (from David Roberts's blog)

• Added description of the representing object of $I$-indexed camilies of equicontinuous functions into $U$, and proof that the limit-selection function for convergent nets is continuous with respect to this uniformity.

• I created separator, while having the nagging feeling that we already have this entry. Of course after creating it I remembered the page generator.

So we should merge the stuff. Might this be an occasion to merge away from generator? A set of “generating objects” also means other things than “separating objects” (notably colimit generation). So I’d be inclined to move all material to separator. That would also allow to drop the warning at the beginning of generator.

• am splitting this off from Lie algebra, for ease of cross-linking.

• Page created, but author did not leave any comments.

• 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

• B. Andrei Bernevig, Taylor L. Hughes, Shou-Cheng Zhang, Quantum spin Hall rffect and topological phase transition in HgTe quantum wells, Science 15 December 2006: 314, n. 5806, pp. 1757-1761 doi

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.

• Clean up a couple parenthetical remarks. The page ring object seems to indeed have the desired diagrams.

• at KLT relations I have expanded the list of references. I added also references for the generalization of these relations that is known these days as “gravity is Yang-Mills squared” or similar (eventually this might want to be a separate entry).

In this course I also expanded the list of references at quantum gravityAs a perturbative quantum field theory

• started a bare minimum at Poisson-Lie T-duality, for the moment just so as to have a place to record the two original references

• In Idea, added “commutative” to the type of C*-algebras appearing in refresher of Gelfand Duality

• $A\times B$ is not the coproduct of $A$ and $B$ in Rel.

Anonymous

• I noticed that the entry classifying space is in bad shape. I have added a table of contents and tried to structure it slightly, but much more needs to be done here.

I have added a paragraph on standard classifying spaces for topological principal bundles via the geometric realization of the simplicial space associated to the given topological group.

In the section “For crossed complexes” there is material that had been provided by Ronnie Brown which needs to be harmonized with the existing Idea-section. It proposes something like a general axiomatics on the notion of “classifying space” more than giving details on the geometric realization of crossed complexes

• A stub entry, for the moment just to have a place to record

I had wanted to extract the main definition and theorem from the article into the entry, but got distracted with editing at good open cover instead, and now am out of time for tonight. More later…

• Corrections in the last section

Matteo Capucci

• Adding model structure from cubical type theory.

• this used to be inside 4-sphere. Am giving it its stand-alone entry for ease of listing references

• I added to Galois connection the remark that some authors call an adjunction between posets a *monotone Galois connection* and a dual adjunction between posets an *antitone Galois connection*.
• Todd,

when you see this here and have a minute, would you mind having a look at monoidal category to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?

Thanks!

• This is not a composition between functors but a composition between applications of the functors

• In response to an email sent to Urs by Andrew Marshall, a slight amendment to good open cover was made in the proof that paracompact manifolds admit good open covers.

• Updated the linkref weak initial algebras' toweak inital’ (a.k.a. ‘weakly initial’)

• Corrected the reference to where Lurie shows that the tangle hypothesis may be deduced from the cobordism hypothesis.

• I felt like the (∞,1) section should give an abstract description rather than a model specific one, so I’ve done so, and proved in the abstract the equivalence between the hom-space and slice-category characterizations.

It feels like cheating to invoke the Grothendieck construction for it; can the argument be made just as cleanly without it?

… I’m having trouble with the formatting, so I’m going to do some bisection to track down the issue….