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- Discussion Type
- discussion topicsemiclassical state
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 21st 2013

Just in case you see me editing in the

*Recently Revised*list and are wondering:I have created and have started to fill some content into

*semiclassical state*. But I am not done yet and the entry is not in good shape yet. So don’t look at yet it unless in a mood for fiddling and editing.

- Discussion Type
- discussion topicclassical-to-quantum notions - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 21st 2013

I started an entry

*classical-to-quantum notions - table*for inclusion in “Related concepts”-sections in the relevant entries.This is meant to clean up the existing such “Related concepts”-lists. But I am not done yet with the cleaning-up…

- Discussion Type
- discussion topicsemiclassical+approximation
- Category Latest Changes
- Started by zskoda
- Comments 10
- Last comment by Urs
- Last Active Mar 21st 2013

New entry semiclassical approximation. It requires a careful choice of references. The ones at the wikipedia article are catastrophically particular, 1-dimensional, old and non-geometric and hide the story more than reveal. Stub Maslov index containing the main references for Maslov index.

- Discussion Type
- discussion topicGalois topos
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by zskoda
- Last Active Mar 21st 2013

I created Galois topos following Dubuc’s article.

But I must be missing something about the notation: does it really mean to say that $A$ is an $\Delta Aut(A)$-torsor, as opposed to saying that it is

*associated*to an $\Delta Aut(A)$-torsor?

- Discussion Type
- discussion topicLagrangian dg-submanifold
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Mar 20th 2013

I have added the relations

coisotropic submanifold $\leftrightarrow$ Lagrangian submanifold in Poisson Lie algebroid

Dirac structure $\leftrightarrow$ Lagrangian submanifold in Courant Lie 2-algebroid

to

*Lagrangian submanifold*and cross-linked with various related entries, such as*polarization*.

- Discussion Type
- discussion topicEmpty entries
- Category Latest Changes
- Started by Tim_Porter
- Comments 16
- Last comment by TobyBartels
- Last Active Mar 20th 2013

There have been two empty pages created lately, both anonymous. They are at Riemann sphere and quasi inverse. It looks as if both were attempts to add something that was aborted.

- Discussion Type
- discussion topicwall crossing in Aarhus
- Category Latest Changes
- Started by Tim_Porter
- Comments 5
- Last comment by Tim_Porter
- Last Active Mar 20th 2013

This page, wall crossing in Aarhus, refers (in the future tense) to a course in 2010. The webpage link is broken as well. Does anyone have a link that could replace that one?

- Discussion Type
- discussion topicNew page: [[finitely generated object]]
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by IngoBlechschmidt
- Last Active Mar 19th 2013

A stub, so that I could link to it from the Café. Redirects from finitely presented object. (Is there any connection with finitely presentable object?) The general definition may not be the best, please check!

- Discussion Type
- discussion topicstrange entries
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by TobyBartels
- Last Active Mar 19th 2013

Thought I would flag up that there have been two of these lately, ideal in semigroups and liars paradox. I waited to see if their ‘authors’ were going to come back and correct them, but so far they have not.

The entry Mochizuki's proof of abc is non-standard in form but has been updated by someone called Daniel.

- Discussion Type
- discussion topicPoisson tensor
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 18th 2013

created

*Poisson tensor*just for completeness, to be able to point to it from related entries.

- Discussion Type
- discussion topic(co)isotropic subspaces - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 18th 2013

created a simple table

*(co)isotropic subspaces - table*for inclusion in other entries, just so as to usefully cross-link the relevant entries

- Discussion Type
- discussion topicholonomy groupoid
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 15th 2013

Added a little to the Idea-section of

*holonomy groupoid*. But this deserves to be further expanded upon.

- Discussion Type
- discussion topicmodel structure on dg-algebras over an operad
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 14th 2013

am starting model structure on dg-algebras over an operad

- Discussion Type
- discussion topicDiscrete event systems
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Mar 13th 2013

I created a stub for discrete event system as the grey link on tropical semirings was annoying me!

- Discussion Type
- discussion topic"The" category of sets
- Category Latest Changes
- Started by Todd_Trimble
- Comments 27
- Last comment by TobyBartels
- Last Active Mar 12th 2013

Mentions of the category $Set$ occur all over the nLab, but with quite a bit of plasticity of meaning. I thought it might be good to have another look at the entry Set and try to describe this plasticity as considered along various axes, to help readers who might be puzzled by “just what does the nLab think the category of sets is?” For example, one reads that the category of sets has marvelous properties such as being a well-pointed topos, and then a little further down one sees that $Set$ is not a topos according to predicative mathematics. This could be very confusing. Similarly, there are some pages in the nLab that assume $Set$ satisfies AC without batting an eye, while others discuss arcane weaker choice principles that $Set$

*might*satisfy. I think we need to be a just a bit more up-front about this, right on the page Set.In the definition section on Set, I made a meager start on this by declaring that the nLab adopts a ’pluralist’ position on the matter of sets and $Set$, and jotted down a few of the possible axes (“axises”, if I were James Dolan) of meaning and interpretation that guide how one thinks of $Set$, e.g., predicative vs. impredicative, classical vs. intuitionist, selection of choice principles, and others. I didn’t think really hard about this, but it might suggest useful ways of organizing the page.

I left out other axes such as “structural vs. material”, and said nothing about type theory. The page set talked more about this; I envision Set as concentrating more on properties of the category of sets.

I got to thinking about this when I began to wonder how Toby thinks about $Set$, which is maybe different from how I usually think about it. (Usually it feels slightly alien to me to posit say WISC as a possible choice principle for the

*category of sets*, which for me usually connotes a model of ETCS – normally I’d think of WISC instead as a possible axiom for a topos or a pretopos.) I was wondering whether Toby had a kind of “bottom line” for $Set$, say for example “$Set$ for me means at least a well-pointed topos with NNO, unless I choose to adopt a predicative mode”, or something like that. Anyway, discussion is invited.

- Discussion Type
- discussion topicAbsolute differential forms
- Category Latest Changes
- Started by TobyBartels
- Comments 32
- Last comment by TobyBartels
- Last Active Mar 10th 2013

After a few days’ editing, I’m announcing absolute differential form (using my neologism). This is a notion of differential form that can be integrated on a completely

*unoriented*submanifold. Examples from classical differential geometry include the arclength element on a Riemannian manifold and ${|\mathrm{d}z|}$ on the complex plane.Since there are classical examples, people must have thought about these before me, but I have never heard of them. Absolute differential forms are not linear (although they must satisfy a restricted linearity condition), and many typical examples are not smooth (although they are still continuous), so they don’t show up in the usual classification theorems. Has anybody heard of them before?

- Discussion Type
- discussion topicKostant-Souriau extension
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 9th 2013

created brief remark at

*Kostant-Souriau extension*(beware the hyphen bug, sometimes only

*Kostant Souriau extension*will work, not sure why and when)(the hyphen bug combined with the cache bug combined with the low responsiveness make for a special experience…)

- Discussion Type
- discussion topicN-complex
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Mar 6th 2013

New stubs N-complex (the homological algebra where $d^N = 0$ with $N\gt 2$) and Michel Dubois-Violette. This interested me somewhat over a decade ago. Unfortunately, I missed the seminar talk yesterday in Zagreb by one of my colleagues, Pavle Pandžić, who found with his collaborator, very recently, that a more general and more insightful redefinition of Dirac cohomology, suggested by concrete applications in representation theory, involves the homological algebra of $N$-complexes. I hope there will be some writeup soon available.

- Discussion Type
- discussion topicLinear independence
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Mar 3rd 2013

I made linearly independent subset to satisfy a link. I put in something about the free-forgetful adjunction and something else about constructive mathematics.

- Discussion Type
- discussion topicsite
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Tim_Porter
- Last Active Feb 28th 2013

expanded a bit the discussion of morphisms of sites at site

- Discussion Type
- discussion topicn-groups
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Mirco Richter
- Last Active Feb 26th 2013

There was a parity error at n-group; I fixed that and put in the low-dimensional examples.

- Discussion Type
- discussion topicArtin-Mazur codiagonal
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active Feb 24th 2013

I have created a diambiguation entry at Artin-Mazur codiagonal, as the old links at bisimplicial set lead to the entry on the codiagonal of a coproduct. I have used total simplicial set as the preferred term. Perhaps a more detailed discussion of this might be useful, but I have not got the time at the moment. (I am very slow at doing diagrams, :-( )

- Discussion Type
- discussion topicgeneric proofs and AC
- Category Latest Changes
- Started by Mike Shulman
- Comments 16
- Last comment by Mike Shulman
- Last Active Feb 22nd 2013

Wrote generic proof with some comments about a couple seemingly weaker versions of the axiom of choice that I've never seen mentioned anywhere before (has anyone else?). Toby and I noticed these a little bit ago while thinking about exact completions, but I just now realized that they're actually good for something: proving that the category of anafunctors between two small categories is essentially small (in the "projective" way).

- Discussion Type
- discussion topicTruth eventually and almost everywhere
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Feb 19th 2013

I wrote eventuality filter, although maybe this was unnecessary, and as it was mostly already there at net. Then I took some of the logic from there and adapted it to null set.

- Discussion Type
- discussion topicfree field theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Feb 18th 2013

created

*free field theory*with the formalization in terms of BV-complexes by Costello-Gwilliam.

- Discussion Type
- discussion topicThomason's homotopy colimit theorem
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active Feb 16th 2013

Does anyone know if we have a discussion, somewhere, of the theorem of Thomason linking homotopy colimits with Grothendieck constructions. I have looked in places that I thought were likely but found no trace of it, but sometimes things get buried in entries on other topics so are difficult to find.

- Discussion Type
- discussion topiccritics of string theory
- Category Latest Changes
- Started by zskoda
- Comments 60
- Last comment by Urs
- Last Active Feb 15th 2013

New entry critics of string theory to collect the references on controversies. I think they are often rambling and vague, not technically useful s the main references we want to collect under string theory and books in string theory. I have changed the sentence in string theory about mathematical definition of parts to somewhat more precise

But every now and then some aspect of string theory, some mathematical gadget or consequence found there is isolated and redefined independently and mathematically rigorously, retaining many features originally predicted.

The point is that most often one does not make rigorous the way some thing is defined via string theory, but one isolates an invariant of manifolds for example and defines a similar one via completely different foundations. The typical example is quantum cohomology which is defined in geometric terms and not in terms of field theory any more.

I have one disagreement with the entry: it says that topological quantum field theory has been discovered as part of string theory research, This is not true, TQFTs were found in 1977, 1978, 1980 articles of Albert Schwartz which had nothing to do with string theory. Only much later Atiyah’s formulation is influenced by string theory.

- Discussion Type
- discussion topicThe convenient setting of global analysis
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Feb 13th 2013

I finally gave

*The convenient setting of global analysis*a*category: reference*-entry. Started adding pointers to it from the References-section of some relevant entries. But there will be many more left.

- Discussion Type
- discussion topicNew discussion stub: [[weak enrichment]]
- Category Latest Changes
- Started by TobyBartels
- Comments 7
- Last comment by Urs
- Last Active Feb 12th 2013

I moved some discussion from bicategory to weak enrichment, a new page. (Possibly it was already moved somewhere else, since Mike had already deleted it, but I couldn't find it.)

- Discussion Type
- discussion topicoperad for modules over an algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 12th 2013

some basic definitions at

*operad for modules over an algebra*and*operad for bimodules over algebras*

- Discussion Type
- discussion topicSegal's category
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Feb 11th 2013

created

(but did we have this already as an entry under some other name?)

Hm, the apostrophe in the page title comes out in unicode, I didn’t create it that way…. And strange things happen now when linking to it. There is a link to this page at simplex category for instance which works just fine. But something tends to go wrong…

- Discussion Type
- discussion topictensor product of infinity-modules
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 11th 2013

I have started to extract some of the relevant key steps from

*Higher Algebra*into*tensor product of infinity-modules*.For me that currently mainly serves as an index for how to find those needles in the haystack. But eventually I should turn it into a more comprehensive discussion.

(Some of this used to be over at bilinear map, but I have now moved it).

- Discussion Type
- discussion topicmorphism of (infinity,1)-operads
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 11th 2013

Just some definitions from

*Higher Algebra*:with some pointers to infinity-algebra over an (infinity,1)-operad, etc. Also to

*microcosm principle*(more on that in a moment).

- Discussion Type
- discussion topicreflective (oo,1)-subcategory
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by Marc Hoyois
- Last Active Feb 9th 2013

added to the Properties-section of reflective (infinity,1)-subcategory the statement and detailed proof of the fact that reflective (oo,1)-subcategories are precisely the full subcategories on local objects.

This proof is really not specific to (oo,1)-categories and parallels a corresponding proof for 1-categories essentially verbatim. A similar 1-categorical proof I had once typed into geometric embedding. I should really copy either one of these versions to reflective subcategory.

- Discussion Type
- discussion topicfiber and cofiber
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by IngoBlechschmidt
- Last Active Feb 8th 2013

- Discussion Type
- discussion topicrigidification
- Category Latest Changes
- Started by hilbertthm90
- Comments 13
- Last comment by Mike Shulman
- Last Active Feb 8th 2013

I just learned about rigidification and decided to record it somewhere.

I’m not sure if the title is good, because there is the notion of the rigidification of quasi-categories.

Surely this notion has a higher analogue that maybe someone knows more about. Surely you could take an $n$-stack and consider the $n$-categorical fiber product to make a notion of inertia, and then rigidify with respect to some subgroup object inside…

- Discussion Type
- discussion topicreduced scheme
- Category Latest Changes
- Started by IngoBlechschmidt
- Comments 2
- Last comment by Urs
- Last Active Feb 8th 2013

Added to

*reduced scheme*a characterization of reducedness by the internal language of the corresponding sheaf topos: A scheme $X$ is reduced iff its structure ring $\mathcal{O}_X$ is a residue field in the internal sense of $\mathrm{Sh}(X)$.

- Discussion Type
- discussion topicinfinity-CS theory for binary non-degenerate invariant polynomial - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2013

created a table

*infinity-CS theory for binary non-degenerate invariant polynomial - table*adapted from

- Pavol Ševera,
*Some title containing the words “homotopy” and “symplectic”, e.g. this one*

and included it into the relevant entries

- Pavol Ševera,

- Discussion Type
- discussion topicLie differentiation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2013

I filled a general-abstract definition into

*Lie differentiation*. Mainly I took the key points from the beginning of*Formal moduli problems*and reviewed them a notation somewhat more streamlined to Lie-theoretic reasoning. Then I added an indicaton of how differential cohesion fits in. More should be added to the entry.I’ll see how much time and energy I have left.

- Discussion Type
- discussion topicdeformation context
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2013

- Discussion Type
- discussion topic(∞,2)-category of ∞-algebras and ∞-bimodules
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 4th 2013

Just in case you see this in the

*Recently Revised*-announcement and are wondering:I was beginning to extract the key steps in the construction of the $(\infty,2)$-category of $A_\infty$-algebras and $A_\infty$-bimodules internal to a suitable monoidal $\infty$-category that is in section 4.3 of

*Higher Algebra*.I have strated to make some notes in this direction at

*bimodule – Properties – (∞,2)-category of bimodules*and at*bilinear map – For ∞-modules*.But this is taking more work than I thought and I need to postpone this until next week (and change my plans for our seminar tomorrow…). Therefore for the moment this material sits there “under construction”. Please take that into account if you look at it at all.

(On the other hand, if anyone feels like lending a hand in completing this, I’d sure be happy about it. I’ll come back to this later this week).

- Discussion Type
- discussion topicTannaka duality: structure on algebras and their module categories - table
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 4th 2013

I am constructing a table

*structure on algebras and their module categories - table*and am including it into the relevant entries. This is a bit experimental for the moment. More details and variants should be added and maybe some of the relations stated in a better way. Help is appreciated.

- Discussion Type
- discussion topic2-ring
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Feb 4th 2013

I find the concept-formation for

*2-rings*in- Alexandru Chirvasitu, Theo Johnson-Freyd,
*The fundamental pro-groupoid of an affine 2-scheme*(arXiv:1105.3104)

particularly clear-sighted. Among other things it improves on the rationale for considering associative algebras as 2-modules/2-vector spaces and sesquialgebras as 2-rings/3-modules/3-vector spaces.

Where Baez-Dolan defined a “2-rig” to be a compatibly monoidal cocomplete category, theses authors observe that one should require a bit more and define a 2-ring to be a compatibly monoidal presentable category. (This follows Jacob Lurie’s discussion, some of which is alluded to at Pr(infinity,1)Cat).

I have now written out some of the basic definitions and statements at 2-ring in a new subsection

*Compatibly monoidal presentable categories*. I also re-organized the full Definition section a bit, adding a lead-in discussion.- Alexandru Chirvasitu, Theo Johnson-Freyd,

- Discussion Type
- discussion topicPuiseux series
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Urs
- Last Active Feb 4th 2013

I added some material to Puiseux series, notable the proof that for $K$ algebraically closed of characteristic zero, they form the algebraic closure of the field of Laurent series $K((x))$. This is to be connected with a number of unwritten topics like Hensel’s lemma, Newton polygon, complete local ring, and others.

Meanwhile, I noticed that the term “local field” has, besides physics meanings, two closely related distinct mathematical meanings. One for which we have a page local field is (non-discrete) “locally compact Hausdorff topological field”, but another is “field of fractions of a complete DVR”. It’s somewhat strange that two such closely related but distinct concepts have the same name – a terrible source of confusion.

- Discussion Type
- discussion topic2Mod
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 3rd 2013

I found we needed an entry

*2Mod*such as to be able to say things like “a sesquialgebra is an algebra internal to $2Mod$”.So I started something.

- 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.