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    • starting an entry on the integer Heisenberg group.

      For the moment it remains telegraphic as far as the text is concerned (no Idea-section)

      but it contains a slick (I find) computation of the modular transformation of Chern-Simons/WZW states from the manifest modular automorphy of certain integer Heisenberg groups.

      Hope to beautify this entry a little more tomorrow (but won’t have much time, being on an intercontinental flight) or else the days after (where I am however at a conference, but we’ll see).

      v1, current

    • The cotangent complex theorem

      Natalie Stewart

      diff, v3, current

    • Adding the actual definition.

      Natalie Stewart

      diff, v5, current

    • I have added to orthogonal factorization system

      1. in the Definition-section three equivalent explicit formulations of the definition;

      2. in the Properties-section the statement of the cancellability property.

      Wanted to add more (and to add the proofs). But have to quit now. Maybe later.

    • Mentioned the alternative terminology “Zappa–Szép product” and added redirects.

      diff, v5, current

    • At the old entry cohomotopy used to be a section on how it may be thought of as a special case of non-abelian cohomology. While I (still) think this is an excellent point to highlight, re-reading this old paragraph now made me feel that it was rather clumsily expressed. Therefore I have rewritten (and shortened) it, now the third paragraph of the Idea-section.

      (We had had long discussion about this entry back in the days, but it must have been before we switched to nForum discussion, because on the nForum there seems to be no trace of it.)

    • added section labels and a table of contents

      Anonymous

      diff, v6, current

    • starting page on antithesis partial orders

      Anonymouse

      v1, current

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

      v1, current

    • starting page on zero-dimensional rings

      Anonymouse

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • starting page on rings with tight apartness

      Anonymouse

      v1, current

    • tried to polish one-point compactification. I think in the process I actually corrected it, too. Please somebody have a close look.

    • the entry braid group said what a braid is, but forgot to say what the braid group is; I added in a sentence, right at the beginning (and fixed some other minor things).

    • brief category:people-entry for hyperlinking references

      v1, current

    • as mentioned in another thread, I have expanded the Idea-section at polarization in order to highlight the relation to canonical momenta (which I also edited accordingly).

    • there is an old article (Berends-Gastman 75) that computes the 1-loop corrections due to perturbative quantum gravity to the anomalous magnetic moment of the electron and the muon. The result turns out to be independent of the choice of (“re”-)normalization (hence what they call “finite”).

      I have added a remark on this in the (g−2)(g-2)-entry here and also at quantum gravity here.

    • I have been expanding and polishing the entry Heisenberg group.

      This had existed in bad shape for quite a while, but now it’s maybe getting into better shape.

      I tried to spend some sentences on issues which I find are rarely highlighted appropriately in the literature. So there is discussion now of the fact that

      • there are different Lie groups for a given Heisenberg Lie algebra,

      • and the appearance of an “ii” in [q,p]=i[q,p] = i may be all understood as not picking the simply conncted ones of these;

      I also added remarks on the relation to Poisson brackets, and symplectomorphisms.

      In this context: either I am dreaming, or there is a mistake in the Wikipedia entry Poisson bracket - Lie algebra.

      There it says that the Poisson bracket is the Lie algebra of the group of symplectomorphisms. But instead, it is the Lie algebra of a central extension of the group of Hamiltonian symplectomorphisms.

    • starting page on inequality rings or rings with inequality

      Anonymouse

      v1, current

    • starting page on apartness rings

      Anonymouse

      v1, current

    • starting page on residually discrete local rings

      Anonymouse

      v1, current

    • working on writing out how the “inversion” morphism of a groupoid object naturally arises from this structure.

      Jonathan Beardsley

      diff, v54, current

    • The entry test category which I wrote some time ago, came into the attention of Georges Maltsiniotis who kindly wrote me an email with a kind praise on nlab and noting that his Astérisque treatise on the topic of Grothendieck’s homotopy theory is available online on his web page and that the Cisinski’s volume is sort of a continuation of his Astérisque 301. Georges also suggested that we should emphasise that a big part of the Pursuing Stacks is devoted to the usage of test categories, so I included it into the bibliography and introductory sentence. I hinted to Georges that when unhappy with a state of an nlab entry he could just feel free to edit directly.

    • Have added to pushout-product the statement (here) that pushout product □\Box of I 1I_1-cofibrations with I 2I_2-cofibrations lands in (I 1□I 2)(I_1\Box I_2)-cofibrations; and (here) the example of pushout products of the inclusions S n−1↪D nS^{n-1} \hookrightarrow D^n. Both without proof for the moment.

    • brief category:people-entry for hyperlinking references

      v1, current

    • Added a paper:

      • Joseph A. Goguen, What is a concept?, (2005). In: Dau, F., Mugnier, ML., Stumme, G. (eds) Conceptual Structures: Common Semantics for Sharing Knowledge. ICCS 2005. Lecture Notes in Computer Science, vol 3596. Springer, Berlin, Heidelberg, (pdf)

      diff, v11, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • creating a stub entry, for now just to make the link work, and to have a home for references specific to abelian CS

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Added a few additional descriptions of □ ≤1\Box_{\leq 1}, which is the same as Δ ≤1\Delta_{\leq 1}.

      diff, v18, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I fixed a link to a pdf file that was giving a general page, and not the file!

    • Tried to improve the wording of the first paragraph.

      diff, v7, current

    • the book Monoidal Functors, Species and Hopf Algebras is very good, but still being written. Clearly the current link under which it is found on the web is not going to be the permanent link. So I thought it is a bad idea to link to it directly. Instead I created that page now which we can reference then from nLab entries. When the pdf link changes, we only need to adapt it at that single page.

    • I felt that we had too many gray links to metalanguage, so I gave it a try. But I don’t really have the leisure for it now and not the expertise anyway. Experts please feel invited to take apart what I wrote there and replace with it something better.

    • added an Idea-section to Mackey functor (which used to be just a list of references). Also added more references.

    • added some indication of the actual construction, below the statement of the theorem.

      (This might deserve to be re-organized entirely, but I don’t have energy for this now.)

      diff, v23, current

    • In the past we had some discussion here about why simplicial methods find so much more attention than cubical methods in higher category theory. The reply (as far as I am concerned at least) has been: because the homotopy theory = weak oo-groupoid theory happens to be well developed for simplicial sets and not so well developed for cubical sets. Historically this apparently goes back to the disappointment that the standard cubical geometric realization to Top does not behave as nicely as the one on simplicial sets does.

      Still, it should be useful to have as much cubical homotopy theory around as possible. Many structures are more naturally cubical than simplicial.

      So as soon as the Lab comes up again (we are working on it...) I want to create a page model structure on cubical sets and record for instance this reference here:

      Jardine, Cubical homotopy theory: a beginning

    • a category:reference-page for the constructive algebraic topology software

      v1, current

    • Added a bit, including the original reference by G. B.

      diff, v7, current

    • Table of Markov categories, to be included in the relevant pages. (This way updates are included in all relevant pages.)

      v1, current

    • added pointer to:

      • Rob Norris, Functional Programming with Effects, talk at Scala Days 2018 [video: YT]

      diff, v56, current

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