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- Discussion Type
- discussion topicsesquialgebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 3rd 2013

started

*sesquialgebra*(It’s about time to add some material on how these are 3-modules/3-vector spaces. )

- Discussion Type
- discussion topicCartan-Dirac structure on a Lie group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 3rd 2013

- Discussion Type
- discussion topicHenselian ring
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Todd_Trimble
- Last Active Feb 2nd 2013

unmotivated stub for Henselian ring

- Discussion Type
- discussion topicGaussian probability distribution
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Feb 2nd 2013

created

*Gaussian probability distribution*, just for completeness

- Discussion Type
- discussion topicloop group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 2nd 2013

stub for loop group

- Discussion Type
- discussion topicConstruction of enriched end requires enrichment cat to be closed?
- Category Latest Changes
- Started by joe.hannon
- Comments 6
- Last comment by Todd_Trimble
- Last Active Feb 1st 2013

In End of V-valued functors, a construction is given for the end of a V-enriched functor, which references an adjunction between hom-sets and tensor products. But the article assumes only that the enrichment category V is only symmetric monoidal, not a closed monoidal, so by what right do we have this adjunction? I'm assuming that this is just an oversight and the additional assumption on V should be added (this seems to be what Kelly's book does), can you confirm?

- Discussion Type
- discussion topicRenormalization and Effective Field Theory
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by zskoda
- Last Active Jan 31st 2013

have started an entry Renormalization and Effective Field Theory on Kevin Costello’s book

- Discussion Type
- discussion topictopological subspace
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Todd_Trimble
- Last Active Jan 28th 2013

the term

*topological subspace*used to redirect to the general-purpose entry*subspace*. I have now instead made it redirect to*subspace topology*and pointed to there from*subspace*.(Also, at

*subspace*I have removed a sentence which claimed that “On the nLab we often say ’space’ to mean ’topological space’.” Because on the contrary, on the $n$Lab we are dealing with general abstract mathematics and not just the small field of topology, and so we are being careful and don’t assume that “space” by default means “topological space”.)

- Discussion Type
- discussion topicvirtual particle
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by TobyBartels
- Last Active Jan 27th 2013

stub for

*virtual particle*, just for completeness

- Discussion Type
- discussion topicvolume
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by TobyBartels
- Last Active Jan 27th 2013

created

*volume*, just for completeness

- Discussion Type
- discussion topicmonoidal functor
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Tobias Fritz
- Last Active Jan 26th 2013

the entry monoidal functor did not state the axioms. I put them in.

- Discussion Type
- discussion topicLarry Lambe
- Category Latest Changes
- Started by Tim_Porter
- Comments 9
- Last comment by jim_stasheff
- Last Active Jan 25th 2013

I created an entry on Larry Lambe. I included a link to some (on line) notes of his on Symbolic Computation which includes discussion of the perturbation lemma from homological perturbation theory.

- Discussion Type
- discussion topicmanifold structure of mapping spaces
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by DavidRoberts
- Last Active Jan 25th 2013

I looked again after a long while at the entry

*manifold structure of mapping spaces*, looking for the statement that for $X$ a compact smooth manifold and $Y$ any smooth manifold, the canonical Frechet structure on $C^\infty(X,Y)$ coincides with the canonical diffeological structure.So this statement wasn’t there yet, and hence I have tried to add it, now in

*Properties – Relation between diffeological and Frechet manifold structure*.To make the layout flow sensibly, I have therefore moved the material that was in the entry previously into its own section, now called

*Construction of smooth manifold structure on mapping space*.While re-reading the text I found I needed to browse around a good bit to see where some definition is and where some conclusion is. So I thought I’d equip the text more with formal Definition- and Proposition environments and cross-links between them. I started doing so, but maybe I got stuck.

Andrew, when you see this here and have a minute to spare: could you maybe check? I am maybe confused about how the $\{P_i\}$ and $\{Q_i\}$ are to be read and what the index set of the charts of $C^\infty(M,N)$ in the end is meant to be. For instance from what you write, what forbids the choice of $\{P_i\}$ and $\{Q_i\}$ being the singleton consisting just of $M$ and $N$ itself, respectively?

- Discussion Type
- discussion topicaction (physics) - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 24th 2013

felt the need to include the following table into various entries, so I created it as an Include-file

*action (physics) - table*

- Discussion Type
- discussion topiccartesian functor
- Category Latest Changes
- Started by Mike Shulman
- Comments 9
- Last comment by TobyBartels
- Last Active Jan 24th 2013

In light of confusion about different possible meanings, I changed cartesian functor to be largely a disambiguation page. Feel free to object.

- Discussion Type
- discussion topicmoment
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 23rd 2013

stub for

*moment*, just for completeness

- Discussion Type
- discussion topicWick's lemma
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 23rd 2013

created stub for

*Wick's lemma*, for the moment just so as to record a pointer to a reference

- Discussion Type
- discussion topicsquare roots of line bundles - table
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 22nd 2013

I have started another table:

*square roots of line bundles - table*, and included it into relevant entries

- Discussion Type
- discussion topicHamilton-Jacobi equation
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active Jan 22nd 2013

One of the formalisms in variational calculus and in particular a formulation of classical mechanics (and also a version for geometrical optics, with eikonal in the place of principal function) is Hamilton-Jacobi equation which just got an entry.

Eventually, I would like to transform somehow the entry classical mechanics. Namely if we fill the sections which are there written but empty, it will grow beyond usability. I think apart from introduction, the entry should have passage between various formalisms. But the details on each formalism could be better on the separate page. Now the bulk of the entry is Poisson formalism which should be I think a separate entry. But it is not easy to engineer a good plan for this yet so let us continue adding material and we can transform the overall logic later. In any case, Hamilton-Jacobi formalims should be on equal footing with Hamiltonian formalism, Lagrangean formalism, Poisson formalism, Newton formalism etc. and some exotic structures like Nambu mechanics and Routhians should be mentioned and linked, in my opinion.

- Discussion Type
- discussion topicperturbation theory with factorization algebras
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 22nd 2013

I have added some more pointers to work by Owen Gwillian on perturbation theory with factorization algebras to

- Discussion Type
- discussion topicLogical functor
- Category Latest Changes
- Started by DavidRoberts
- Comments 13
- Last comment by Mike Shulman
- Last Active Jan 22nd 2013

I changed the definition at logical functor, as it said that such a thing was a cartesian functor that preserved power objects. The page cartesian functor says

A strong monoidal functor between cartesian monoidal categories is called a cartesian functor.

which really is only about finite products, not finite limits as Johnstone uses, which I guess is where the definition of logical functor was lifted from. So logical functor now uses the condition ’preserves finite limits’.

So I added a clarifying remark to cartesian functor that the definition there means finite-product-preserving, and that the Elephant uses a different definition.

However, people may wish to have cartesian functor changed, and logical functor put back how it was. I’m ok with this, but I don’t like the terminology cartesian (and I’m vaguely aware this was debated to some extent on the categories mailing list, so I am happy to go with whatever people feel strongest about).

- Discussion Type
- discussion topicHofer geometry
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jan 21st 2013

New entry Helmut Hofer and changes or references at related entries like polyfold and Hofer’s geometry which also got a redirect Hofer geometry (which seems to be prevalent version these days).

- Discussion Type
- discussion topicBerezinian (superdeterminant)
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by zskoda
- Last Active Jan 21st 2013

Just a stub superdeterminant, aka Berezinian. Added a reference to quasideterminant and universal localization. Extended the list of related entries at matrix.

- Discussion Type
- discussion topiccomplex path integral
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jan 21st 2013

Recent topic of analytic continuation issues related to path integrals and the playing with complex analogues of action functionals got an entry: complex path integral.

- Discussion Type
- discussion topicoo-Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 53
- Last comment by jim_stasheff
- Last Active Jan 18th 2013

It is clear that infinity-Chern-Weil theory will induce lots of examples of

*oo-Chern-Simons theory*: for every Chern-Simons element on an $\infty$-Lie algebroid $\mathfrak{a}$, there is the corresponding generalized Chern-Simons action functional on the space of $\mathfrak{a}$-valued connections/forms.I have started now listing all the familiar QFTs that are obtained as special cases this way. This is a joint project I am doing with Chris Rogers.

So I started that list with comments and proofs at Chern-Simons element and began creating auxiliary entries as the need was. So there are now some stubs on

(coupling these three yields the 2-Chern-Simons theory for the canonical invariant polynomial on a strict Lie 2-algebra !)

also did

(that entry was due a long time ago)

- Discussion Type
- discussion topic4-3-2 8-7-6
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 18th 2013

Created a

*category:reference*-entry for- Dan Freed,
*4-3-2 8-7-6*, talk at*ASPECTS of Topology*Dec 2012

and linked to it from some relevant entries.

- Dan Freed,

- Discussion Type
- discussion topicChan-Paton gauge field over D-brane and worldsheet anomaly cancellation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 18th 2013

I started discussing the

*Chan-Paton gauge field*and how it cancels the Kapustin-part of the Freed-Witten-Kapustin anomaly for the open string.The technical ingredients are now all there, but I need to fill in more glue text to make this readable. Will do so, but might have to interrupt now. I ran a bit out of time here…

- Discussion Type
- discussion topicLiouville-Poincaré cocycle in cohesive homotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by zskoda
- Last Active Jan 17th 2013

It just occurred to me that there is an immediate axiomatization of the Liouville-Poincaré 1-form (the canonical differential 1-form on a cotangent bundle) in differential cohesion.

In fact, it is the special case of a much more general notion: for $A$ any type in differential cohesion the total space $\underset{X}{\sum} \mathcal{O}_X(A)$ of the $A$-valued structure sheaf over any $X$ carries a canonical $A$-cocycle.

For $A = \Omega^1$ the sheaf of 1-forms and $X$ a manifold, this is the traditional Liouville-Poincaré 1-form on $T^* X$.

I made a quick note on that at

*differential cohesion – Liouville-Poincaré cocycle*.Thanks to a conversation with Owen Gwilliam I now also understand how that construction gives the antibracket in the BV-BRST complex. I still need to write that out. Not today though.

- Discussion Type
- discussion topictensor product of abelian categories
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Tim_Porter
- Last Active Jan 17th 2013

quick note on

*Deligne tensor product of abelian categories*

- Discussion Type
- discussion topicPicard 3-group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 16th 2013

added

*References*to*Picard 3-group*.

- Discussion Type
- discussion topicK-invariant
- Category Latest Changes
- Started by Tim_Porter
- Comments 10
- Last comment by Tim_Porter
- Last Active Jan 16th 2013

Just a comment, I mostly have seen k-invariant, with a lower case k. Does anyone have ‘strong’ feelings about this?

- Discussion Type
- discussion topicextended Lagrangian
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 15th 2013

Since I found myself repeatedly referring to it from other $n$Lab entries, I finally put some content into the entry

*extended Lagrangian*.

- Discussion Type
- discussion topicHigher Algebraic Structures and Quantization
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 14th 2013

I needed a Reference-entry for Freed’s old article

*Higher Algebraic Structures and Quantization*, so I created one.

- Discussion Type
- discussion topicstandard model of fundamental physics - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 14th 2013

I am experimenting with a table

But I am still experimenting. I need a table with roughly the content as given there, but loads of things still need attention. The table itself omits some details even of that which it manifestly aims to display and doesn’t display at all yet what one might also list under its title.

Please be gentle to this stub for the moment. I need this for some lecture notes elsewhere and right now am only investing a few minutes into this, need to look into other things with higher priority for the moment. But of course eventually we should prettify this.

- Discussion Type
- discussion topicEinstein-Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 14th 2013

added briefly the definition to

*Einstein-Yang-Mills theory*

- Discussion Type
- discussion topicEinstein-Maxwell theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 14th 2013

added briefly the definition to

*Einstein-Maxwell theory*

- Discussion Type
- discussion topicscalar curvature
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 14th 2013

stub for

*scalar curvature*

- Discussion Type
- discussion topicGrassmannian
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by TobyBartels
- Last Active Jan 14th 2013

I ended up creating brief entries

and cross-linked them a bit. But nothing much there yet.

- Discussion Type
- discussion topicbig bang
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jan 11th 2013

created

*big bang*(really, I was just working on

*field (physics)*, which made me create*scalar field*, then*inflaton*, and now this. That’s how it goes.)

- Discussion Type
- discussion topichyperdeterminant
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jan 10th 2013

New stub hyperdeterminant (I was convinced we had it before, but…no).

- Discussion Type
- discussion topichigher spin structure - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 10th 2013

I keep drawing and re-drawing that Whitehead tower again and again. That needs to stop. So I created now an entry with a table, to be included where needed:

*higher spin structure - table*

- Discussion Type
- discussion topicreduction modality -| infinitesimal shape modality -| infinitesimal flat modality
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Mike Shulman
- Last Active Jan 9th 2013

created little entries

- reduction modality $\dashv$ infinitesimal shape modality $\dashv$ infinitesimal flat modality

to go along with the previous entries

- shape modality $\dashv$ flat modality $\dashv$ sharp modality

(whose $n$Forum-discussion is here)

All of this is part of the cohesion - table.

- Discussion Type
- discussion topicgauge field - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 7th 2013

started

*gauge field - table*and included it into the relevant entries

- Discussion Type
- discussion topicformally smooth object
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 5th 2013

quickly created

*formally smooth object*.Have to go offline now. More later.

- Discussion Type
- discussion topic7d Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 4th 2013

Added a fair bit of content to

*7d Chern-Simons theory*.Of the three examples discussed there, the first two are review. The third is inspired by something I have been talking about with D. Fiorenza, C. Rogers and H. Sati.

- Discussion Type
- discussion topicroots, weights, etc.
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by TobyBartels
- Last Active Jan 3rd 2013

- Discussion Type
- discussion topicIMU
- Category Latest Changes
- Started by zskoda
- Comments 8
- Last comment by TobyBartels
- Last Active Jan 3rd 2013

- Discussion Type
- discussion topicpolylogarithm
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Dec 31st 2012

New stub polylogarithm and many new links at dilogarithm.

- Discussion Type
- discussion topicAndersen and Ueno's proof that geometric quantization = quantum groups
- Category Latest Changes
- Started by Bruce Bartlett
- Comments 10
- Last comment by Urs
- Last Active Dec 27th 2012

- I added a query box to the Holographic Principle page, referring to the work of Andersen and Ueno which I believe has now made rigorous that geometric quantization of Chern-Simons theory = quantum groups approach ala Reshetikhin-Turaev.

- Discussion Type
- discussion topicNew version of anafunctors paper
- Category Latest Changes
- Started by DavidRoberts
- Comments 20
- Last comment by DavidRoberts
- Last Active Dec 25th 2012

Before I forget, I uploaded a new version of my anafunctors paper to my page David Roberts. In particular, the finer points have been made a lot tighter. I even use technical phrases such as ’enough groupoids’ and ’admits cotensors’! :) It has also been submitted for publication.

- Discussion Type
- discussion topicLipschitz continuity
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Dec 23rd 2012

Here it is: Lipschitz map. I don't know why I wrote it; I just felt like it. There really is much more to say, but I think that I've said enough for now!

- Discussion Type
- discussion topicNoetherian poset
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 21st 2012

stub for

*Noetherian poset*(just needed to be able to point to it, no real content there yet)

- Discussion Type
- discussion topicMonique Hakim
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 20th 2012

created people-entry

*Monique Hakim*and cross-linked with*Structured Spaces*

- Discussion Type
- discussion topicstable factorization system
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Dec 19th 2012

added in an Examples-section to

*stable factorization system*the statement that in an adhesive category, in particular in a topos, the (epi, mono)-factorization is stable.

- Discussion Type
- discussion topicCrans-Gray tensor product
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 18th 2012

added to Crans-Gray tensor product a brief remark on the fact that it gives a biclosed monoidal structure.

- Discussion Type
- discussion topicstructure sheaf
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 18th 2012

I have renamed the relevant section at

*differential cohesion*to*differential cohesion – Structure sheaves*, expanded a bit, and linked to it from*structure sheaf*and other related entries.

- Discussion Type
- discussion topiclocally representable structured (infinity,1)-topos
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Stephan A Spahn
- Last Active Dec 17th 2012

I split off locally representable structured (infinity,1)-topos from generalized scheme .

This is about Lurie’s $\mathcal{G}$-schemes, but I decided to change the title. For one to avoid the continuous conflict of notions of “generalized scheme” that made generalized scheme a mess, but also because it seems quite reasonable terminology to. Would’t you agree?

- Discussion Type
- discussion topictopological M5-brane
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2012

stub for

*topological M5-brane*. And now I really have to RUN

- Discussion Type
- discussion topictopological membrane
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2012

I have split off

*topological membrane*from*topological M-theiry/M2-brane*to record a reference. But otherwise no content yet.

- Discussion Type
- discussion topicHitchin functional
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2012

started

*Hitchin functional*but have to interrupt now in the middle of it. This entry is not in good shape yet.