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    • added at Grothendieck universe at References a pointer to the proof that these are sets of κ-small sets for inaccessible κ. (also at inaccessible cardinal)

    • Together with my PhD students, I have been thinking a lot recently about the appropriate notion of a module over a C^∞-ring, i.e., something with better properties than Beck modules, which boil down to modules over the underlying real algebra in this case.

      We stumbled upon the article C-infinity module (schreiber).

      It says: “a C-infty algebra A is a copresheaf AQuantities=CoPrSh(CartesianSpaces) which becomes a copresheaf with values in algebras when restricted along FinSetCartesianSpaces,”

      Why are we restricting to FinSet here? The underlying commutative real algebra is extracted by restricting to the Lawvere theory of commutative real algebras, i.e., CartesianSpaces_Poly, the subcategory of cartesian spaces and polynomial maps. Restricting to FinSet^op (as opposed to FinSet) extracts the underlying set only. It is unclear what is being meant by restricting along FinSet→CartesianSpaces, since the latter functor does not preserve finite products, so restricting along it does not produce a functor between categories of algebras over Lawvere theories.

    • brief category:peopleentry for hyperlinking references

      v1, current

    • Switch commuting reasoning to use an implication for clarity.

      diff, v19, current

    • a bare minimum, for the moment just to make the link work

      v1, current

    • some minimum, for the moment mostly to record this item:

      • Edna K. Grossman: On the residual finiteness of certain mapping class groups, J. London Math. Soc. s2-9 1 (1974) 160–164 [doi;10.1112/jlms/s2-9.1.160]

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Added a link to the retyped version of SGA 4 1/2.

      diff, v15, current

    • Added to T-duality a section with the discussion of the usual path-integral heuristics for why the two sigma-models on T-dual backgrounds yield equivalent quantum field theories.

    • starting page on apartness rings

      Anonymouse

      v1, current

    • splitting this off from su(2)-anyons: Copied much of the material over, but also added a few more sentences.

      For the moment this entry is a cautionary tale about confirmation bias more than an entry about physics.

      v1, current

    • Just noticed that we have a duplicate page Jon Sterling.

      I have now moved the (little but relevant) content (including redirects) from there to here.

      Unfortunately, the page rename mechanism seems to be broken until further notice, therefore I am hesitant to clear the page Jon Sterling completely, for the time being.

      diff, v3, current

    • I looked at real number and thought I could maybe try to improve the way the Idea section flows. Now it reads as follows:

      A real number is something that may be approximated by rational numbers. Equipped with the operations of addition and multiplication induced from the rational numbers, real numbers form a number field, denoted . The underlying set is the completion of the ordered field of rational numbers: the result of adjoining to suprema for every bounded subset with respect to the natural ordering of rational numbers.

      The set of real numbers also carries naturally the structure of a topological space and as such is called the real line also known as the continuum. Equipped with both the topology and the field structure, is a topological field and as such is the uniform completion of equipped with the absolute value metric.

      Together with its cartesian products – the Cartesian spaces n for natural numbers n – the real line is a standard formalization of the idea of continuous space. The more general concept of (smooth) manifold is modeled on these Cartesian spaces. These, in turnm are standard models for the notion of space in particular in physics (see spacetime), or at least in classical physics. See at geometry of physics for more on this.

    • stub for confinement, but nothing much there yet. Just wanted to record the last references there somewhere.

    • brief category:people-entry for hyperlinking references

      v1, current

    • created black holes in string theory, since somebody asked me: a brief paragraph explaining how the entropy-counting works and some references.

    • brief category:people-entry for hyperlinking references

      v1, current

    • have created a stub for supersymmetric quantum mechanics

      Zoran, I see that you once dropped a big query box at quantum mechanics with a complaint. I disagree with the point you make there: we have fundamental definitions of quantum field theory and restricting them to 1 dimension gives quantum mechanics. If you want to turn this around and understand all QFTs as infinite-dimensional quantum mechanics (which, yes, one can do) you are discarding the nice conceptual models and kill the concept of extended QFT.

      In any case, I think remarks like this (in the style of “we can also regard this the other way round like this”) are better added into an entry as what they are – remarks – than as query boxes that give the impression that there is something fishy about the rest of the entry.

    • brief category:people-entry for hyperlinking references

      v1, current

    • Corrected a link. Before the word “derivation” linked to the page for derivations in differential algebra.

      Sam Winnick

      diff, v27, current

    • I came across this tiny page which is called by ’extension’ from the page central extension.

      But what’s this page trying to be? Merely about a certain kind of field extension?

      diff, v3, current

    • Created:

      Idea

      […]

      Related concepts

      References

      Introduced by

      • Wolfgang Soergel, The combinatorics of Harish-Chandra bimodules, Journal für die reine und angewandte Mathematik 429 (1992) 49-74. doi, PDF.

      Survey:

      • Nicolas Libedinsky, Gentle introduction to Soergel bimodules I: The basics, arXiv:1702.00039.

      v1, current

    • This page contains a brief review of the Bousfield–Kan formula and its validity in various settings.

      Kensuke Arakawa

      v1, current

    • Finally noticed that this entry here was a stub without TOC, without references and without cross-links. Have touched it a little.

      diff, v4, current

    • As we discussed, I am orphaning this page and have merged its previous content into page “Bousfield–Kan formula”.

      Kensuke Arakawa

      diff, v13, current

    • Have added to HowTo a description for how to label equations

      In the course of this I restructured the section “How to make links to subsections of a page” by giving it a few descriptively-titled subsections.

    • a stub entry, for the moment just to make the link work

      v1, current

    • briefly recording the “rotation” quantum gates

      v1, current

    • Update the link to Drinfeld’s paper (pdf).

      Anonymous

      diff, v4, current

    • Page created, but author did not leave any comments.

      v1, current

    • I added LaTeX and some text for testing.

      IbrahimMustafa

      v1, current

    • was initially just looking for a page to host this reference:

      but now I wrote a little bit of an Idea-section, too. Leaving much room to be further expanded, of course.

      v1, current

    • made some cosmetic adjustments to the entry,

      and slightly expanded the last remark (which I made a Remark) relating to order theory (prodded by this comment)

      diff, v7, current

    • Added a budget of links from the FAQ to the Eunuch-Code Data-Bank.

      For some odd reason, the TOC generator is not picking up the first heading — ???

    • Created:

      Idea

      An intrinsic notion of an open subobject in an elementary topos.

      Definition

      A monomorphism UX in an elementary topos E is a Penon open if the following statement holds in the internal logic of E:

      xXyX(xU)(¬(y=x)yU).

      Properties

      If UX is a Penon open, then

      xU({yX¬¬(y=x)}U).

      Related concepts

      References

      v1, current

    • added list of publications, as far as currently cited on the nLab (no particular order)

      diff, v6, current