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- Discussion Type
- discussion topicdifferential cohesion and idelic structure
- Category Latest Changes
- Started by David_Corfield
- Comments 24
- Last comment by Urs
- Last Active Jun 25th 2015

There doesn’t seem to be a discussion for this page differential cohesion and idelic structure. Is this to be the general page for ’inter-geometry’?

If so, it might be worth recording An Huang, On S-duality and Gauss reciprocity law, (Arxiv).

- Discussion Type
- discussion topiceta invariant
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jun 24th 2015

added to

*eta invariant*a lightning section*On manifolds with boundaries: as sections of the determinant line*, essentially just a glorified pointer to Freed 95 for the time being.

- Discussion Type
- discussion topicTambara functor
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by David_Corfield
- Last Active Jun 23rd 2015

Began stub for Tambara functor. Neil Strickland’s,

*Tambara Functors*, arXiv:1205.2516 seems to be a good reference.Seems like it’s very much to do with pullpush through polynomial functors, if you look around p. 23.

I would try to say what the idea is, but have to dash.

- Discussion Type
- discussion topicintermediate model structure
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by Mike Shulman
- Last Active Jun 20th 2015

Created intermediate model structure. Needs more cross-linking, but I have to go.

- Discussion Type
- discussion topicWZW-model globalized over Cartan geometry -- elementary formalization
- Category Latest Changes
- Started by Urs
- Comments 40
- Last comment by Urs
- Last Active Jun 19th 2015

In two recent threads [1, 2] I had started to look into elementary formalization of the following obstruction problem in higher geometry:

given

a Klein geometry $H \to G$,

a WZW term $\mathbf{L}_{WZW} : G/H \longrightarrow \mathbf{B}^{p+1} \mathbb{G}_{conn}$;

a Cartan geometry $X$ modeled on $G/H$

then:

- what is the obstruction to globalizing the WZW term to $X$?

Here are first concrete observations, holding in any elementary $\infty$-topos (meaning: this may be proven using HoTT, not needing simplicial or other infinite diagrams):

First, a lemma that turns the datum of a global WZW term $Fr(X) \longrightarrow \mathbf{B}^{p+1}\mathbb{G}_{conn}$ on the frame bundle of $X$ (each of whose fibers looks like the formal disk $\mathbb{D}$ around the base point, or any other point, in $G/H$) into something closer to cohomological data on $X$. In the following $Fr(X)$ may be any fiber bundle $E$ and $\mathbf{B}^{p+1}\mathbb{G}_{conn}$ may be any coefficient object $A$.

**Lemma.**Let $E \to X$ be an $F$-fiber bundle associated to an $Aut(F)$-principal bundle $P \to X$. Then $A$-valued functions on $E$ are equivalent to sections of the $[F,A]$-fiber bundle canonically associated to $P$.**Proof.**By the discussion at*infinity-action*, the universal $[F,A]$-fiber bundle $[F,A]/Aut(F)\to \mathbf{B} Aut(F)$ is simply the function space $[F,A]_{\mathbf{B} Aut(F)}$ formed in the slice over $\mathbf{B} Aut(F)$, with $F$ regarded with its canonical $Aut(F)$-action and $A$ regarded with the trivial $Aut(F)$-action.Now, by universality, sections of $P \underset{Aut(F)}{\times} [F,A] \to X$ are equivalently diagonal maps in

$\array{ && [F,A]/Aut(F) \\ & \nearrow & \downarrow \\ X & \longrightarrow & \mathbf{B} Aut(F) }$But by Cartesian closure in the slice and using the above, these are equivalent to horizontal maps in

$\array{ E & = & P \underset{Aut(F)}{\times} F && \longrightarrow && A \times \mathbf{B}Aut(F) \\ && & \searrow && \swarrow \\ && && \mathbf{B}Aut(F) }$Finally by $(\underset{\mathbf{B}Aut(F)}{\sum} \dashv \mathbf{B}Aut(F)^\ast)$ this is equivalent to maps $E \to A$. $\Box$

$\,$

[ continued in next comment ]

- Discussion Type
- discussion topiccomplex volume
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by DavidRoberts
- Last Active Jun 19th 2015

am splitting off

*complex volume*from*hyperbolic manifold*

- Discussion Type
- discussion topicBloch group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jun 18th 2015

stub for

*Bloch group*

- Discussion Type
- discussion topicDirichlet-Borel regulator
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jun 17th 2015

added details to

*Borel regulator*, with discussion of Becker-Gottlieb transfer and the refinement to differential algebraic K-theory by the transfer index conjecture.

- Discussion Type
- discussion topicodd Chern character
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 17th 2015

started some minimum at

*odd Chern character*and cross-linked a little

- Discussion Type
- discussion topicMichal-Bastiani smooth map
- Category Latest Changes
- Started by DavidRoberts
- Comments 4
- Last comment by DavidRoberts
- Last Active Jun 17th 2015

I created Michal-Bastiani smooth map, and linked to it from diffeological space, Andree Ehresmann and locally convex topological vector space.

- Discussion Type
- discussion topicBHK interpretation
- Category Latest Changes
- Started by Todd_Trimble
- Comments 5
- Last comment by Mike Shulman
- Last Active Jun 15th 2015

Very stubby beginning of BHK interpretation.

- Discussion Type
- discussion topicWitt-Burnside functor
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Jun 10th 2015

Started Witt-Burnside functor.

- Discussion Type
- discussion topiccoprojections
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Jun 8th 2015

I split off coprojection from projection and added a remark about their monicity (or lack thereof).

- Discussion Type
- discussion topicQuandles and racks
- Category Latest Changes
- Started by John Baez
- Comments 4
- Last comment by John Baez
- Last Active Jun 4th 2015

- Discussion Type
- discussion topicExchangeability
- Category Latest Changes
- Started by David_Corfield
- Comments 7
- Last comment by Urs
- Last Active Jun 3rd 2015

I added a new section to Bayesian reasoning, Exchangeability, which outlines the de Finetti Representation theorem. As indicated, there’s a multivariate version. This was used to talk about Bose-Einstein statistics.

I wonder if anything interesting would happen with a HoTT rendition of statistical meachanics.

- Discussion Type
- discussion topichollymolly spam
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by DavidRoberts
- Last Active Jun 3rd 2015

Someone has got the Euler-Lagrange equation page to redirect to hollymolly, and added that word at the bottom. How do we undo such vandalism?

- Discussion Type
- discussion topichomothety
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 30th 2015

during a talk on homotheties of Cartan geometries that I heard yersterday, it occurred to me that this concept has an immediate simple general abstract formulation in differential cohesive homotopy theory. Made a note on this now at

*homothety*.

- Discussion Type
- discussion topicFirst slide syndrome!
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active May 30th 2015

- Discussion Type
- discussion topicBorger's absolute geometry
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active May 29th 2015

Added to

*F1*a section*on Borger’s absolute geometry*and then split it off as a stand-alone entry (minimal as it is)*Borger’s absolute geometry*.

- Discussion Type
- discussion topicgeometry of physics -- prequantum geometry
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 29th 2015

I have been working on filling genuine content into

The first part

*Infinitesimal symmetries*should be about readable, it starts out plenty expositionary, I hope, but towards the end it is still very terse. I wanted to get much further today, but it didn’t work out that way.

- Discussion Type
- discussion topicdg-Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 28th 2015

There was an ancient query box discussion sitting in the entry

*dg-Lie algebra*which hereby I am moving from there to here.

begin of ancient discussion

+–{: .query}

Tim: I have changed the wording that Zoran suggested slightly. Of course, a dgla is an internal Lie algebra, a term that needs making precise in an entry, but then we must make precise the tensor product, and the symmetry. All that abstract baggage is, of course, in other entries, but I think it best to avoid the term ’simply’. I have heard it expressed that category theorists tend to use the term ’simply’ aand other similar terms too much from the point of view others working in neighbouring disciplines.

For instance, if someone knows de Rham theory from a geometric viewpoint, we know that in the long run it will be useful for them to understand the differential graded algebra from a categorical viewpoint as that is one of the most fruitful approaches for geometrically significant generalisations and applications BUT the debutant can get very put off by thinking that they have to understand lots of category theory before they can start understanding the de Rham complex. In fact coming from that direction they can understand the category theory via the de Rham theory. So I suggest that we simply avoid ’simply’!!

I know some researchers in other subject areas are looking with interest to the nLab as a quick means of entry into some interesting mathematics and a handy reference for definitions and background. That is great but it perhaps means that we have to be a bit careful about our natural feeling that the categorical approach is nearly always the ’best’. ’Simply’ is one problem, another is, I think, use of diagrams rather than formulae. My feeling is that both should be given (though the diagrams are more difficult to get looking nice).

Urs: these are all good points. In general I believe it will be good to offer different perspectives in an $n$Lab entry, and explain what they are useful for, each. I take the point that the word “simply” for the categorical perspective may raise unintended feelings, so maybe it should be avoided or at least not left uncommented.

But we should also not hide the important point here, which is hinted at by the word simply: I think that the important point is that the abstract category-theoretic formulation which packages a long list of detailed definitions in a single statement such as “internal Lie algebra” allows us to recognize that that list of definitions is

*right*.There are many definitions that one can dream up. But some are better than others and category theory can explain why.

For instance I have seen experts who calucalted with differential graded algebra all day long be mystified by why exactly all the sign rules are as they are. The best explanation they had was: it works and yields interesting results. They were positively interested to learn that

*all*these signs follow automatically and consistently by realizing that differential graded algebra is algebra internal to the category of chain complexes.This doesn’t mean that it is best to introduce DGCA in this internal language. But it does mean that it is worthwhile pointting out that lots of nitty-gritty details of definitions can “simply” be derived by starting with an abstract internal definition and then turning the crank.

Tim: I could not have put it better myself. I was wondering if there might not be some way in which this viewpoint might not be expressed explicitly. Perhaps David C has some thoughts.. sort of ’the unreasonable effectiveness of categorical language’?

My intention for my own contribution (with help hopefully) is to gradually add glosses in the lexicon entries so as to help interpret in both directions, categorically,and geometrically.

For instance, in the construction of the cobar one take the tensor algebra of the suspension of the cokernel (is it?) of the augmentation. WHY?!!!!!!! How can one understand this? Magic? It works? In fact it is still a bit of a mystery to me and saying that it comes from such and such a categorical property still needs spelling out for me. I have asked rational homotopy theorists and have partially understood things from their point of view but there are still gaps in my understanding of it and some of them worry me!

*Toby*: One should be able to say something like, ’From a category-theoretic perpsective, a differential graded Lie algebra is simply an internal Lie algebra in an appropriate category of chain complexes.’. This advertises what Urs says, that definitions come automatically from the category-theoretic perspective, without pretending that this will be simple to anyone coming from outside that perpsective.Zoran Škoda: Tim, your question about the intricacies of cobar construction in the category of chain complexes is an interesting one, which I can not fully answer, specially in a short answer. However, still the categorical picture simplifies the viewpoint and the definition at least,and gives a direction how to proceed there as well. Given a dgca C one looks at the functor Tw(C,A) assigning to an algebra A the set of solution of the Maurer-Cartan equation $d t + t*t = 0$ where $*$ is the convolution product. Cobar construction is the (co)representative of this covariant functor. If you take Tw(C,A) as a contravariant functor on the coalgebras, for fixed A, then its representative is the bar construction (this is said in different words in entry twisting cochain). So bar and cobar construction are simply representatives of very natural functors; accidents of the realization of these functors by formulas in Ch are a bit unfortunate as you pointed out.

=–

end of ancient discussion

- Discussion Type
- discussion topiccartographic group
- Category Latest Changes
- Started by Noam_Zeilberger
- Comments 7
- Last comment by Noam_Zeilberger
- Last Active May 27th 2015

I created a stub page for cartographic group, with definitions and a reference. The not-yet-existent article was already linked to from child’s drawing.

- Discussion Type
- discussion topicWKB or semiclassical
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by Urs
- Last Active May 26th 2015

I wanted to add some references on WKB approximation, but found that we have two entries semiclassical approximation and WKB method. WKB or semiclassical expansion is one and the same thing: asymptotic expansion of quantum mechanical amplitudes in Planck constant. On the other hand, “WKB method” is often used to limit considerations just to the stationary phase approximation way of doing the expansion, rather than say to the path integral equivalent (the latter anyway used mainly in physics treatments of semiclassical expansion only).

- Historically WKB or WKBJ (J for Jeffreys) method or approximation has been studied only in one dimension till works of Maslov and others in late 1950s, when the multidimensional analogue has been found. The asymptotics of wave type equations has been studied more generally by Maslov, Hoermander and others as the theory of Fourier differential operators where the stationary phase approximation is the main tool. Mathematically, WKB is precisely the stationary phase approximation and it has been used much earlier in optics as so called geometrical optics approximation.

One can “historically” limit to just one dimension and just to asymptotics of integral expressions in first order, so in some sense one can limit to some particular case as WKB approximation, but for a modern researcher, WKB and semiclassical method is one and the same thing. I can hardly split the discussion and references to the two entries, so I would rather have them merged into one entry and restrict any mention of the difference in scope to a historical subsection. What do you think about it (Urs, especially). (In fact it makes some sense to rename WKB method entry into 1-dimensional WKB method and to discuss just the old early theory there).

- I see that the table in semiclassical approximation says that formal deformation is in all orders while semiclassical just in first (or finite? not clear from the table) order. This is not true, semiclassical expansion is sometimes considered to all orders. But it is an expansion of complex valued functions understood as asymptotic series, and summability issues and analysis of rapidly oscillating functions is in the center of attention. Thus formal means formal, in the sense of formal power series. Semiclassical is asypmtotic expansion, not only formal. Nothing to do with first order !

At semiclassical approximation, I added references on so called exact WKB method, very popular recently, stemming from Voros 1983, where one looks at WKB expansion to

*all orders*and understands it in the sense of Borel summability.A. Voros,

*The return of the quartic oscillator. The complex WKB method*, Annales de l’institut Henri Poincaré A39:3, 211-338 (1983) euclidAlexander Getmanenko, Dmitry Tamarkin,

*Microlocal properties of sheaves and complex WKB*, arxiv/1111.6325Kohei Iwaki, Tomoki Nakanishi,

*Exact WKB analysis and cluster algebras*, J. Phys. A 47 (2014) 474009 arxiv/1401.7094;*Exact WKB analysis and cluster algebras II: simple poles, orbifold points, and generalized cluster algebras*, arXiv:1409.4641

- Discussion Type
- discussion topicmathematical economics
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 22nd 2015

arc spaces from Nash’s work reminded me of Nash equilibrium so I wrote the stub for mathematical economics. I added also a reference relating some model in that field to tropical geometry.

- Discussion Type
- discussion topicgeometry of physics -- BPS charges
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 21st 2015

am working on a new chapter of the

*geometry of physics*cluster:Still a bit rough towards the end, but I need a break now.

In the course of this I started splitting off a further chapter

*geometry of physics – prequantum geometry*, but that’s rudimentary at the moment.

- Discussion Type
- discussion topicmonadic descent
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active May 20th 2015

Zoran created monadic descent

- Discussion Type
- discussion topicShelah's main gap
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by Todd_Trimble
- Last Active May 20th 2015

sorry, first created it in David Corfields’ web, then in $n$Lab. DId not keep track where I was.

- Discussion Type
- discussion topicD-brane geometry
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 20th 2015

I gave

*D-brane geometry*a minimum of content and references. This is what in string theory was called “D-geometry” in the glory 90s and so I added a disambiguation line at the top of the latter entry.

- Discussion Type
- discussion topiccoalgebraic logic
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by David_Corfield
- Last Active May 19th 2015

We did not have the page on coalgebraic logic so I just created as a place for links for now, we could expand on it later.

- Discussion Type
- discussion topicco-Kleisli category
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active May 19th 2015

started

*co-Kleisli category*with a minimum of content. Even though its formally dual to*Kleisli category*, of course, it may be worthwhile to have a separate entry.

- Discussion Type
- discussion topicrandom variable
- Category Latest Changes
- Started by Urs
- Comments 43
- Last comment by NikolajK
- Last Active May 18th 2015

I have created

*random variable*with some minimum context.In addition I have added pointers to Kolmogorov’s original book and to some modern lecture notes to

*probability theory*and some related entries.I have briefly cross-linked

*probability space*with*possible worlds*, indicating a similarity of concepts and an overlap of implementations.

- Discussion Type
- discussion topicgeometry of physics -- WZW terms
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 14th 2015

I am working on a further chapter of

*geometry of physics*titled*geometry of physics – WZW terms*.So far there is just the introduction.

As usual, in the course of this I will be touching related entries. Right now I have copied the bulk of that introduction also to the entry

*WZW model*in the section*Topological term – WZW term – For the 2d WZW model*, replacing the material that was there before (which I had had written, too, but the new version is better).

- Discussion Type
- discussion topichomotopy monomorphism
- Category Latest Changes
- Started by adeelkh
- Comments 3
- Last comment by adeelkh
- Last Active May 13th 2015

Created a new entry homotopy monomorphism.

- Discussion Type
- discussion topicinfinitesimal disk bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 13th 2015

finally gave

*infinitesimal disk bundle*its own entry.

- Discussion Type
- discussion topicevolutionary vector field
- Category Latest Changes
- Started by mhohmann
- Comments 2
- Last comment by Urs
- Last Active May 12th 2015

Added page for evolutionary vector field and explained how the two different definitions are related. This follows a discussion here on this paragraph.

- Discussion Type
- discussion topicdifferential operator
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 12th 2015

added to

*differential operator*the characterization via bundle maps out of a jet bundle, together with the note that this means that differential operators are equivalently morphisms in the co-Kleisli category of the Jet bundle comonad.

- Discussion Type
- discussion topiccocompletion
- Category Latest Changes
- Started by zskoda
- Comments 9
- Last comment by Tim_Porter
- Last Active May 9th 2015

I look at ind-cocompletion and pro-completion issues these days. New entry cocompletion. References at many related entries. Notably (at inaccessible cardinal)

- Andreas Blass, Ioanna M. Dimitriou, Benedikt Löwe,
*Inaccessible cardinals without the axiom of choice*, Fund. Math. 194 (2007) 179-189 pdf

We consider four notions of strong inaccessibility that are equivalent in ZFC and show that they are not equivalent in ZF.

(Strange: if I paste ZF and ZFC in font from the Fundamenta page abstract, the nForum truncates everything starting with ZF. This way I lost part of the text which I wrote after this.)

Note that the wikipedia and some other sources have an outdated link for the Blass et al. paper, at a Dutch site. This pdf link is to the Polish Fundamenta site, and works as of now.

- Andreas Blass, Ioanna M. Dimitriou, Benedikt Löwe,

- Discussion Type
- discussion topicprojective plane
- Category Latest Changes
- Started by Mike Shulman
- Comments 12
- Last comment by Mike Shulman
- Last Active May 8th 2015

I made projective plane less stubby.

- Discussion Type
- discussion topicsuperisometry
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 8th 2015

I have been touching, adding references and little pointers, but otherwise nothing real substantial, the following entries:

superisometry group (new but stubby), Killing spinor, BPS state, M-brane, black brane, M9-brane, KK-monopole

and maybe others.

- Discussion Type
- discussion topicZariski site
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by DavidRoberts
- Last Active May 8th 2015

In the Idea section of Zariski site, I included a little patch which includes the little site notion, as well as the big site.

- Discussion Type
- discussion topiclocal diffeomorphism
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by zskoda
- Last Active May 5th 2015

had need for a stub for local diffeomorphism

- Discussion Type
- discussion topicNames of objects and universes
- Category Latest Changes
- Started by Michael_Bachtold
- Comments 32
- Last comment by Mike Shulman
- Last Active May 5th 2015

Prompted by this discussion, I added a minimal explanation of the terminology “name of an object” to the page universe in a topos, right below the first diagram. Please feel free to correct if this is not right.

Since there are several pages talking about universes I also don’t know if that’s the best place for that edit.

- Discussion Type
- discussion topicwall crossing
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Apr 30th 2015

I have edited and expanded

*wall crossing*a littleOne question to Zoran:

you have designed the entry to cover the notion in great generality. But most of the references that you already had, and now also all that I have added, concern wall crossing of BPS states. Eventually we need to do something to make the entry more systematic on this point. Should we split off an “wall crossing of BPS states”, maybe?

- Discussion Type
- discussion topictype II supersymmetry algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 29th 2015

am starting

*type II supersymmetry algebra*to go in parallel with*M-theory supersymmetry algebra*. But not much there yet.

- Discussion Type
- discussion topicDescartes
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 29th 2015

added to

*Descartes*as section*On space, matter and mechanics*with some quotes on Descartes’ picture of mechanism.(I was looking for sources that would argue clearly that Descartes’ mechanism is closer to modern continuum mechanics than to modern point particle mechanics. I found something, but I imagine there might be better such sources still.)

- Discussion Type
- discussion topicvan Est isomorphism
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 28th 2015

I had thought we had an entry on the

*van Est isomorphism*, but maybe we didn’t. Have started a bare minimum, just so as to have the link.

- Discussion Type
- discussion topichomotopy localization and A1-homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by David_Corfield
- Last Active Apr 28th 2015

- Discussion Type
- discussion topicgeometry of physics -- manifolds and orbifolds
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 23rd 2015

I am beginning to work on a new chapter

*geometry of physics – manifolds and orbifolds*.The goal for today is to write detailed exposition of how the theory of manifolds and their frame bundles is set up using the infinitesimal shape modality on the Cahiers topos.

So far I have (only) the

*Introduction*and the first two subsections*Formal smooth Cartesian spaces*and*Formal smooth sets*and some scattered material following that. But now first some lunch break.

- Discussion Type
- discussion topicModern Physics in Modal Homotopy Theory
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Apr 23rd 2015

This week I am at a workshop in Bristol titled

*Applying homotopy type theory to physics*, funded by James Ladyman’s “Homotopy Type Theory project”. David Corfield is also here. The program does not seem to be available publically, but among the other speakers that the $n$Lab community knows is also Jamie Vicary.Myself, I will give a survey talk titled “Modern physics formalized in Modal homotopy type theory” (which maybe should rather have “to be formalized” in the title, depending on how formal you take formal to be). I am preparing expanded notes to go with this talk, which I am keeping at

This is still a bit rough at some points, but that’s how it goes.

I currently also have a copy of the core of this material in one section at

*Science of Logic*, replacing the puny previous section on formalization that was there. While it’s not puny anymore, now maybe it’s too long and should be split off. But just for the time being I’ll keep it there.If you look at it, you’ll recognize a few points that I tried to discuss here lately, more or less successfully. This here is not meant to force more discussion about this – we may all be happier with leaving it as it is – it’s just to announce edits, in case anyone watching the RecentlyRevised charts is wondering.

- Discussion Type
- discussion topicright Bousfield delocalization
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Apr 20th 2015

I created the article right Bousfield delocalization.

- Discussion Type
- discussion topiccompletely distributive Boolean algebras
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Apr 18th 2015

I wrote a subsection at completely distributive lattice on the case of Boolean algebras, showing that they are the same as complete atomic Boolean algebras.

- Discussion Type
- discussion topicLogic as the Essence of Philosophy
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 17th 2015

I gave Russell’s

*Logic as the Essence of Philosophy*(that David keeps citing elsewhere) a category:reference-entry and cross linked a little, for instance linked to it from*logic – References - general*.

- Discussion Type
- discussion topicinfinite product
- Category Latest Changes
- Started by Mike Shulman
- Comments 19
- Last comment by NikolajK
- Last Active Apr 16th 2015

A little bit of a page at infinite product, mainly just a definition, which leads me to ask a question: how do we define convergence of an infinite product in constructive mathematics? The definition seems to depend on decidability of $=0$.

- Discussion Type
- discussion topiclooping and delooping
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Apr 16th 2015

started an entry looping and delooping in an attempt to bring statements together in one place that are currently a bit scattered over the $n$Lab. Not done yet, but need to quit now.

- Discussion Type
- discussion topicequivalence of (2,1)-categories
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 16th 2015

needed a dedicated page

*equivalence of (2,1)-categories*for expositional purposes, so I created it.

- Discussion Type
- discussion topicHodge conjecture
- Category Latest Changes
- Started by adeelkh
- Comments 1
- Last comment by adeelkh
- Last Active Apr 15th 2015

I created a new page integral Hodge conjecture and linked from Hodge conjecture.

- Discussion Type
- discussion topictractor bundle
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Apr 15th 2015

added some actual content to

*tractor bundle*

- Discussion Type
- discussion topicempty 145
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Apr 15th 2015

Someone anonymous set up a file with ’Home Page/solution set condition’ as its name. It was empty so I have renamed it empty 145.

- Discussion Type
- discussion topicWZW-model
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Apr 15th 2015

created stub for WZW model in reply to a question by a colleague (on how to obtain the Hilbert space of states in that model)

- Discussion Type
- discussion topichigher geometry
- Category Latest Changes
- Started by Urs
- Comments 37
- Last comment by Urs
- Last Active Apr 14th 2015

I restructured the (stubby) entry higher geometry a bit, following the logic of big and small toposes.

The point being: you can

either axiomatize geometric structure

*on*a little $\infty$-topos. That’s what the definition of structured (infinity,1)-toposes aims to achieve.or axiomatize geometric structure

*in*a big $\infty$-topos. That’s what the definition of cohesive (infinity,1)-topos aims to achieve.