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    • Edited the first sentence to something more informative, moved Klein’s own texts from “References” to “Writings” and adjusted a little.

      diff, v5, current

    • brief category:reference entry on Bredon’s book, for ease of hyperlinking

      v1, current

    • Changed the page name to “REF MakkaiReyes77” and gave the bullet item an anchor of the same name, such that one can point to it after it is included anywhere.

      This format “AuthornameYear” seems a decently robust identification. I have been using this for anchor names to rference items on the nLab for long time now.

      diff, v2, current

    • am starting some minimum. Not done yet…

      v1, current

    • In the article exterior+algebra, in sect. 2, subsection In General, it says that the nth exterior power of an object VV is the cokernel of the antisymmetrization operator

      P A=1n!∑ σ∈S nsgn(σ)σ. P_{A} = \frac{1}{n!} \sum_{\sigma \in S_{n}} \mathrm{sgn}(\sigma) \sigma.

      Shouldn’t the exterior algebra be the image of this operator? If so, I am happy to edit the article accordingly.

    • I have adjusted the formatting to harmonize with established convention (bullet item).

      Added clarification that the new pdf version is due to and with contributions by Francisco Marmolejo and gave the direct pointer to the pdf, too.

      Will !include this now at logic.

      diff, v2, current

    • I just included a link into this new page, but it needs to be announced at the nLab.

      diff, v2, current

    • Nikolai Durov’s 132-page technical document on Telegram Open Network uses type theory notation in some paragraphs on the currently developing Telegram’s version of ’5-th generation’ blockchain technology, and claims to use in fact the Martin-Loef’s type theory. In the update I also included the link to the ’whitepaper’ and the technical document.

      I also gave a link to the first of a series of 3 papers of Durov to appear in Algebra i analiz, though only the abstract, the first page and the references seem to be downloadable at the moment. There seem to be no arXiv or other public version and the official site of the St. Petersburg Journal of Mathematics is 3 issues backwards till the actual appearance there. Their title is Homotopy theory of normed sets. Its contents generalize part of the formalism from

      • Paugam F., Overconvergent global analytic geometry, 2015, arXiv:1410.7971v2

      diff, v16, current

    • added pointer to the essay Missed opportunities from 1972. What a remarkable document and what an enjoyable read! (I had never looked at this before.)

      diff, v6, current

    • added missing cross-link with cyclic set.

      Some harmonizing might be necessary here, maybe entries should actually be merged.

      diff, v4, current

    • I made the definition of linear interval explicit at interval, also correspondingly streamlined slightly the corresponding text at classifying topos.

    • A stub on computer software Cadabra.

      v1, current

    • updated “counterxample” link from its ancient nForum location

      diff, v9, current

    • I noticed that Welcome to the nForum (nlabmeta) instructed users to make query boxes. I believe query boxes are now deprecated, so I removed that instruction.

    • Added pointers to the Hanany-Witten construction and cross-linked with new section at NS5-brane on D-branes ending on NS5-branes.

      diff, v6, current

    • For the discussion at Higgs field I created a category:people entry for Philip Gibbs, who was about the first to discuss the Higgs detection at LHC.

      diff, v1, current

    • There has been much attention in the nlab on groupoid cardinality of Leinster/Berger and Euler characteristics of a category of Leinster; and Baez's work with collaborators on groupoidification and his earlier talks and posts on cardinality. Urs noticed that it fits with Freed's ideas on Feynman path integrals and came up with Freed-Schreiber-Ulm "kantization" formulas. While this works well for some finite and TQFT situations, I would like to know what happens in general. Tom and Simon Willerton have been doing infinite extensions to metric spaces and heat-kernel like expressions were important there. This reminded me of the equivariant localization formulas of Atiyah-Bott, Duisterman-Heckmann, Witten and others which are used in a number of situations but also computing the first term in heat-like expansions for Feyman integrals. In nice examples, like WZNW model, TQFTs, Chern-Simons, the semiclassical expressions give exact result. That is why the "kantization" in its present version gievs a good result. But we should go beyond. Thus we should understand similar expansions from nPOV. So I started creating some elementary background entries (for a while) like semiclassical approximation and now something closer to topologically oriented people on the blog: Lefschetz trace point formula. Soon there will appear various related index formulas and equivariant index formulas.

      I should tell in advance: the usual Lefschetz formulas are for the traces for one mapping; the equivariant ones are for family index by elements of a group. So it is not a number but a numbered valued function on the group. Thus we are arriving to a character. How now about the case when the group is categorified and we have categorified traces ? In that case we should formulate an appropriate ellipticity notion for a complex of operators on 2-bundles, and come after a categorified index formula. And then to get the G-equivariant version for G a 2-group. Some good kantization formulas should come from index formulas of that kind. By transgression, of course, it should be related to ideas like index formula on loop space, like Witten's index theorem; and eventually also to elliptic cohomology. Right ?

      Edit: yet another thing are anomalies. We took some formulation of anomaly cancellation directly from geometric condition on equipping the space with a particular structure, which then boils down to lift and voila some (nonabelian) obstruction. But originally one looks at amplitudes in QFT, does various standard things to them like zeta function regularization and finds obstruction from there. This took some development in works of Alvarez-Gaume, Jackiw, Stora, Witten and so on, with the role of the geometry of determinant line bundle emphasised by Quillen, Atiyah-Singer, Freed...We did not really go to these origins, and we should I think.

    • mirror symmetry (needs more well chosen references, I am runnning out of time and will be busy next few days; there are hundereds of references available so we should choose important and/or well written ones)

    • Over in another thread, David Roberts asks for explanation of a bunch of terms in QFT (here).

      In reaction I have started a minimum of explanation for one more item in the list: hidden sector.

    • Edit to: Ángel Uranga by Urs Schreiber at 2018-04-01 01:00:59 UTC.

      Author comments:

      added pointer to string pheno textbook

    • Edit to: Luis Ibáñez by Urs Schreiber at 2018-04-01 01:00:18 UTC.

      Author comments:

      added pointer to string pheno textbook

    • Edit to: D6-brane by Urs Schreiber at 2018-04-01 00:53:41 UTC.

      Author comments:

      hyperlinked pointer to textbook by Ibaney-Uranga

    • Edit to: Taub-NUT space by Urs Schreiber at 2018-04-01 00:53:00 UTC.

      Author comments:

      hyperlinked pointer to textbook by Ibaney-Uranga

    • Page created: bullet cluster by Urs Schreiber at 2018-03-31 00:53:25 UTC.

      Author comments:

    • Page created: proof of the prime number theorem by Todd Trimble at 2018-03-31 00:45:16 UTC.

      Author comments:

      New page which gives the details of the proof of the prime number theorem, as extracted from Zagier (after Newman), but less compressed.

    • On the orthogonal group page, there is a table of π i(SO(n))\pi_i(SO(n)) for 1≤i≤121 \leq i \leq 12 and 2≤n≤122 \leq n \leq 12. The reference given is the Encyclopedic Dictionary of Mathematics which actually has a table which goes up to i=15i = 15 and n=17n = 17. In a comment to my last MO question, David Roberts suggested that I add these additional groups to the table. I am happy to do this, but as the person who created the table used the same resource, they made a decision to stop at i=12i = 12 and n=12n = 12; maybe there was a good reason for this.

      Should I expand the table or is it fine as is?

    • Added to simple group an example I was given on MO: the simple group of cardinality κ\kappa, given by taking the smallest normal subgroup of Aut(κ)Aut(\kappa) containing the 3-cycles. This is essentially the ’even’ permutations for an infinite set.

      This is nice, because I was trying to think of a simple group (or one with only small normal subgroups) with inaccessible cardinality, and some obvious tricks weren’t working.

    • I decided to make my first contributions to the nLab, so am following the request, and saying what I did here.

      I fixed a typo in the definition of composition of correspondences. It is now a little unclear, so I also started a new page, internal tensor product (the link was already there, just no page). I’ll try to add some details tomorrow when I have time.

    • Has anyone developed models for the homotopy theory of HℚH \mathbb{Q}.module spectra over rational topological spaces a bit?

      I expect there should be a model on the opposite category of dg-modules over rational dg-algebras. Restricted to the trivial modules it should reduce to the standard Sullivan/Quillen model of rational homotopy theory. Restricted to the dg-modules over ℚ\mathbb{Q} it should reduce to the standard model for the homotopy theory of rational chain complexes, hence equivalently that of HℚH \mathbb{Q}-module spectra.

      Is there any work on this?

    • I added to endomorphism the observation that in a cartesian monoidal category, if an internal endomorphism monoid End(c)End(c) exists and is commutative, then cc is subterminal.

    • Added the following to the page on the Gray tensor product:

      The Gray tensor product as the left Kan extension of a tensor product on the full subcategory Cu of 2Cat is on page 16 of

      Since I’m really new at this, feel very free to give advice or corrections, thanks, Keith

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