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for completeness, I gave formal neighbourhood of the diagonal its own little entry.
Stub for localic completion. I wonder to what extent this can be generalized beyond metric spaces; for uniform spaces or Cauchy spaces we don’t have a nice collection of canonical basis elements like the open balls.
I started an article, surreal number. I’ve run out of energy to put in all the links that should be in there.
I want to get at Conway games at some point, as they are more basic than Conway numbers, and fit well within an nPOV. Conway discovered numbers after games, and it seems only right to establish that priority also within the Lab. In particular, one should mention Joyal’s description of the category of games, and what this has to do with the ordering on numbers.
I have edited the second point under examples on the cogroup page. I replaced what I believe to be an erroneous hTop with hTop*, and have included a reference for the claim that there are cogroups in hTop* which are not suspensions.
am starting an entry tangent complex. For the moment its biggest achievement is to give a pointer to section 8 in Hinich’s invaluable Homological algebra of homotopy algebras .
I have created an entry-for-inclusion Goodwillie calculus - contents, and have included it as a “floating table of contents” into the relevant entries.
I gave Tate spectrum a bare minimum of content.
created analytic (∞,1)-functor.
There is clearly some deep relation here to the Blakers-Massey theorem. But I am not sure yet what the full picture is.
Created a stub entry for norm map, for the moment just so as to make cross-links work.
stub for moduli space of connections, started to collect some references
I have added some bare minimum content to EHP spectral sequence.
I have added some minimum (or not even that) to p-completion. In the process I also created analytic completion and gave fracture theorem an Idea-section.
(None of this is meant to be in the state in which it is, that’s just how far I got in little available time…)
in order toput things in perspective, I created a table
and included it into relevant entries (under “Related concepts”)
I am back to working on geometry of physics. I’ll be out-sourcing new paragraphs there to their own nLab entries as much as possible (because the length of the page makes saving and hence previewing it take many minutes, so I need to work in smaller sub-entries and then copy-and-paste).
In this context I now started an entry prequantum field theory. To be further expanded.
This comes with a table of related concepts extended prequantum field theory - table:
extended prequantum field theory
| 0≤k≤n | transgression to dimension k |
|---|---|
| 0 | extended Lagrangian, universal characteristic map |
| k | (off-shell) prequantum (n-k)-bundle |
| n−1 | (off-shell) prequantum circle bundle |
| n | action functional = prequantum 0-bundle |
Continuing from a very minor edit on localic topos, I've created articles on first-order hyperdoctrines and triposes; both need fleshing out, but the latter in particular I've only just barely started. I intend to add to it a more explicit description of the construction of a topos from a tripos, and discussion of some specific examples (those given by complete Heyting algebras and by realizability relative to a partial combinatory algebra). (Also, the definition has only been given for a special case at the moment).
New entry groupoid quantale so far covering just the construction for the discrete case. But the Resende’s paper cited therein goes of course much beyond.
I gave André Joyal’s lectures in Paris last week their own category:reference page on the nLab, in order to be able to link to them conveniently (from entries such as topos theory and (infinity,1)-topos theory):
I’ve started relational beta-module. It would be lovely if somebody who really grasps it could fill in the abstract definition and maybe check (or even show how to derive) the concrete one, which I extracted from this blog post by Todd Trimble. (Hey, maybe Todd could check it!)
This started when I realised that being infinitely close is a uniform (not topological) property in nonstandard analysis, which is hinted at by the very bottom of the page (as it is now).
Does someone know offhand the relationship between the stabilization hypothesis “for (n,1)-categories” attributed to Joyal and Lurie at stabilization hypothesis and the version that appears in arXiv:1312.3178? It would be nice to add a reference to the latter to the page stabilization hypothesis but I’m not sure how to relate it to what’s already there.
At present the entry EGA is not only about EGA but includes sections on FGA and SGA. Should it be renamed and a new page with that title be created which can do what is said will be done there (e.g. list of chapters etc.).
I have finally added a little bit of substance to Polyakov action (with a little spill-over at Nambu-Goto action).
This is not polished yet, I need to run now and come back to it later.
Someone unhelpfully started Gauss lemma without any content. It was required by good open cover.
According to Wikipedia there needs to be disambiguation.
I am making lots of little edits on F-theory related entries, mostly adding references and pointers to them with brief comments. Hence nothing that deserves much announcement here, but just in case you are watchign the logs and are wondering, I’ll announce some of it anyway, trivial as it may be.
So at supersymmetry and Calabi-Yau manifolds (which exists since long ago but was maybe never announced in the first place, so now it is) I have included a table-for-inclusion titled “N=1 susy compactifications – table”, and also included it then at M-theory on G2-manifolds and at F-theory on CY4-manifolds.
At stable model category I have tried to brush up the section (which is now titled) Properties – As A-infinity algebroid module categories.
Adeel is of course invited to expand further…
added to noncommutative motive a brief version of the Definition due to Blumberg-Gepner-Tabuada.
Also added (with brief comments) their references and the dg-category theoretic precursors by Denis-Charles Cisinski and Tabuada.
(Deserves to be expanded further, certainly, just a quick note so far.)
I have (finally) added some pointers to the result of Freed-Hopkins 13 to relevant nLab entries.
Mostly at Weil algebra – characterization in the smooth infinity-topos
also at invariant polynomials – As differential forms on the moduli stack of connections
pointing out that this adds further rationalization to the construction of connections on principal infinity-bundles – via Lie integration.
In making these edits, I have created and then used a little table-for-inclusion
Presently this displays as follows:
Chevalley-Eilenberg algebra CE ← Weil algebra W ← invariant polynomials inv
differential forms on moduli stack BGconn of principal connections (Freed-Hopkins 13):
CE(𝔤)≃Ω•licl(G)↑↑W(𝔤)≃Ω•(EGconn)≃Ω•(Ω(−,𝔤))↑↑inv(𝔤)≃Ω•(BGconn)≃Ω•(Ω(−,𝔤)/G)I have extracted one of the key statements from
to an entry algebraic K-theory of smooth manifolds.
Someone created a page ’www.emis.de/journals/AM/09-4/roger.ps.gz’. I thought maybe it had come from putting URL before title, but this isn’t so for the three pages which refer to that paper. I’ve changed those three links to the pdf version.
I got tired of not having linear combination, so now we have it.
I created stub for Schwarzian derivative just to record several references.
Someone with pseudonym Z has posted a question at the bottom of a query box at hyperstructure. The question is:
Z: I’d like to know more about composition of bonds as described on p.8 of “Higher Order Architecture of Collections of Objects” (Nils Baas). Can someone please clarify the rules on this page?
I should know this, but now I am getting mixed up, so I'll ask, at the risk of just making a fool of myself:
how do I see whether the transfinite composition of some weak equivalences is again a weak equivalence?
I came across the statement by somebody that SSet has the advantage over Top that weak equivalences are closed under transfinite composition. Then I tried to think about this and found that I got myself mixed up....
Emily Riehl created natural weak factorization system.
I removed the redirect current to conserved current as there is also analysis notion of current (distribution theory) (new entry!). I created a new disambiguation page current and stub integral current. Should write normal current as well and fill some content in the new pages. I added some references for start. One should also relate the conserved current to the page flux and so on.
Added an entry on cocompleteness of varieties of algebras. It surely needs some improvements, but I hope that there are no fatal errors.
Urs helpfully started shell following a conversation at PhysicsForums. It would be handy to add what is meant by ’on-shell’ and ’off-shell’ so we could link over from on-shell recursion and off-shell Poisson bracket and elsewhere.
am starting complex analytic infinity-groupoid (in line with “smooth infinity-groupoid” etc.) and higher complex analytic geometry. Currently there is mainly a pointer to Larusson. To be expanded.
created instanton in QCD
Anders Kock kindly pointed my attention today to remark 7.3.1 in his Synthetic Geometry of Manifolds, which has an observation that goes in the direction of the observation that the jet comonad J∞ is the base change comonad along the map X→ℑX, i.e. along the coequalizer of the two maps out of the formal neighbourhood of the diagonal.
I have added to the entry a quick remark on this.
at signature we should eventually think about some disambiguation. There are many things in math called “signature”- For instance the signature of a permutation.
Made a start on modular lattice.
I created a few stub pages recently: a couple on Saturday for vertex coloring and bipartite graph (thanks to Thomas Holder for a correction and the references), and today the stubbiest of stubs for virtual knot theory.
New stub trigonometry.
Stub for free probability to record some references.
I have added to Kan extension in the section on the pointwise coend formula some elementary illustrative discussion of the case of left Kan extension of presheaves, that some readers might benefit from at this point, see this example.
Someone (at Waldhausen category changed axiom C3) as it was incorrect. The new version still looked wrong, and I have changed it further. (Could someone check that I have got it right now!)
I don’t like the name of the page complete topological space; it seems to suggest that a property of “completeness” can be defined for topological spaces, when in fact one needs additional structure on a topological space (like a metric, a uniformity, or at least a Cauchy structure) in order to say what “complete” means. Since the notion of Cauchy space seems to be the maximum generality in which the notion applies, how about renaming the page to “complete Cauchy space”?
I have been adding some material to Cocomm Coalg. I’m not sure where I first read that this category is extensive, and hope that a relatively painless proof of that can be produced.
It's really the reflection of topological spaces within a larger category, but usually people think of it as underlying: underlying topological space.
have created topos of algebras over a monad
A bit of trivial algebra at trivial subalgebra.
I wrote a constructive definition of simple group, which brought up other issues, so I wrote antisubalgebra and strongly extensional function.
Apparently, the page mathematicscontents, despite being included in a number of other pages, has not existed since shortly after it was spammed slightly more than a year ago. So before blanking a spam page, make sure that it has no history! I have restored it now (although it took a little bit to figure out what it had been called, since it doesn't follow the standard naming format for included contents).
I added a hatnote to syntactic category remarking on an alternative usage of the phrase.
Did some cleaning up and adding to regular category and coherent category, and asked a terminological question at the latter.
I have expanded the text in the entry on Eric Sharpe a little, and added a list of publications. The recent one
reviews and expands on aspects of higher groups/stacks/gerbes in QFT and string theory in a style that ought to appeal to people with physics background.
I came across a non-standard definition of “regular monomorphism” in Cassidy/Hébert/Kelly’s “Reflective subcategories, localizations and factorizations systems.” and added a note to the nlab page. They define a regular mono to be a joint equalizer of an arbitrary family of parallel pairs. This is more general than the usual definition, and forces the class of regular monos to be closed under arbitrary intersections.
I think that in a well powered category with small products the definition should coincide with the usual one, and in coregular categories both should coincide with “strong mono”.
Any comments? Does this definition of regular mono appear anywhere else? Or is there maybe an alternative term for it?