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    • An updated version of the book J-holomorphic Curves and Quantum Cohomology can be found on the web page of Dusa McDuff which is linked at the new entry Dusa McDuff ! I also started a stub symplectic topology and just a little longer one for Floer homology.

    • created Dirac induction with a brief note on the relation to the orbit method, via FHT-II.

    • I started a page about the simplicial bar construction. I haven’t checked all the details carefully (especially regarding 𝒱\mathcal{V}-naturality!) though.

    • Made a start on taut functor. Mike, I mentioned your work with Cruttwell on generalized multicategories in a section on applications.

    • added a brief remark to discrete object in a new section Examples — in infintiy-toposes on the relation between discreteness and cohomology.

      This is a (fairly trivial) comment on Mike’s discussion over on the HoTT blog, linked to from the above.

    • I decided to add some content to the motivic pages here on the nLab.

      I started with Nisnevich site. More to come soon…

    • trivia, but I just ran into this:

      I noticed we have entries:


      both of them referring to operator algebraists. First I thought we need to merge these entries. But after looking around I guess these are indeed two different people. (The German Wikipedia claims here that the second initial of the author of K-Theory for Operator Algebras is “E” not “A”).

      (Notice that the second entry is mistaken, where it says “Home page” it points not to some author’s home page but to the nLab home page…)

      Just making sure. Sorry for the distraction.

    • I was starting to make some notes on the new article by Sergei Gukov and Anton Kapustin, at a new “reference”-categorized entry titled

      Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories

      But so far there is just a vague indication of the main thrust. I want to flesh out more detail later. On the other hand, tomorrow morning I’ll be going on a two week vacation, so this plan will encounter delays.

    • For the sake of illustration I have added to ordinary homology a section In terms of higher linear algebra.

      Currently the main point is to record, after some preliminaries, the standard observation plus detailed proof that for XX a topological space, its ordinary chain complex of singular simplices is, up to equivalence, the \infty-colimit of the tensor unit local system with coefficients in HkModH k Mod. (Its “HkHk-Thom spectrum”.)

    • In the section compacta as algebras, I have written out complete details of a proof that compact Hausdorff spaces are monadic over sets.

    • concerning stable map: is there some nice abstract characterization? Something involving maybe the words “faithful functor of étale groupoids”?

    • Wrote a section General weighted colimit formula at homotopy colimit

      • giving a general formula

      • spelling out the special case of simplicial diagrams, that reproduces the Bousfield-Kan formula

      • spelling out the special case of pushout diagrams, that reproduces the formula (or its dual) discussed more in detail in the other examples that were already present

    • I tried to collect some references at crossed product C*-algebra on their relation to convolution C*-algebras of action groupoids. But I guess I run out of steam…

    • started dual morphism but then began to hesitate: we must have this discussion somewhere already. But where?

    • started a table of contents integration theory - contents and added it as a floating TOC to the relevant entries.

      (Mostly as a reminder to myself to write more on fiber integration in generalized cohomology…)

    • Someone started a page called probability amplitudes but with a single word. I have changed that to say the page is empty. (which of course it is not!) as I did not feel competent to write even a stub on that topic.

    • created models in presheaf toposes with the statement of the fact that T-models in presheaves are presheaves of T-models, at least for T a geometric theory.

      Added a pointer to this from the corresponding discussion at group object.

    • There was some misnumbering (sometimes off by 1, sometimes reversed) at homotopy group#truncconn, which hopefully I've fixed.

    • added to odd line a brief remark on the nature of its automorphism super-group and the consequences, also added some relevant references.

      (I feel like I had added this statement to the nnLab elsewhere already long time ago, but can’t find it now.)

    • I was fixing some Spam at generator and noticed that Grothendieck category has a link to generator, but shouldn’t this be to separator? I have fixed it so that the term generator in Grothendieck category links to separator.

      I tried to clear up some formatting problems / typos at separator. (There is a query near the bottom of the page that seems to still be unanswered.) Can someone glance at the entry to check my reformatting is right as I was on autopilot when doing it!

    • Just now I needed a definition and discussion of term algebra for the new entry on Lindenbaum-Tarski algebra. I noted we have Lindenbaum algebra in several places with no explanation. I am no logician and have very few logic books available. Are these the same and what generality should be used for the term algebra.

      I also looked at the entry on Boolean algebra and was a bit surprised to find there was no elementary algebraic version given. This is the (for dummies) version perhaps, but seeing one of the usual algebraic description and examples (although these are in the Wikipedia page I’m sure) might enable the ideas about Heyting algebras, lattices, etc., there to be more useful. I’m not sure what level to pitch any additions to that entry, any ideas or thoughts anyone?

    • I am going to rewrite a part of the Baer sum, the section “On short exact sequences”, partly following S. MacLane, Homology, 1963 (he does the version for extensions of RR-modules). I am not fully understanding and would like to discuss the issue, but I think the current notation is a bit hiding. So here is the version of the section before my update, so it can be reversed if somebody not happy:

      For 0AG^ iG00 \to A \to \hat G_{i} \to G \to 0 for i=1,2i = 1,2 two short exact sequences of abelian groups, their Baer sum is

      G^ 1+G^ 2+ *Δ *G^ 1×G^ 2 \hat G_1 + \hat G_2 \coloneqq +_* \Delta^* \hat G_1 \times \hat G_2

      The first step forms the pullback of the short exact sequence along rhe diagonal on GG:

      AA AA Δ *(G^ 1G^ 2) G^ 1G^ 2 G Δ G GG \array{ A \oplus A &\to& A \oplus A \\ \downarrow && \downarrow \\ \Delta^* (\hat G_1 \oplus \hat G_2) &\to& \hat G_1 \oplus \hat G_2 \\ \downarrow && \downarrow \\ G &\stackrel{\Delta_G}{\to}& G\oplus G }

      The second forms the pushout along the addition map on AA:

      AA + A Δ *(G^ 1G^ 2) + *Δ *(G^ 1G^ 2) G G \array{ A \oplus A &\stackrel{+}{\to}& A \\ \downarrow && \downarrow \\ \Delta^* (\hat G_1 \oplus \hat G_2) &\to& +_* \Delta^*(\hat G_1 \oplus \hat G_2) \\ \downarrow && \downarrow \\ G &\to& G }
    • I’ve changed Postnikov system definition 2

      the part saying

      “The map Xim n(f)X \to im_n(f) induces an epimorphism on connected components”


      “The map Xim n(f)X \to im_n(f) induces an epimorphism on homotopy groups in degree n1n-1”.

      This was a small issue that confused me.

    • I've seen two meanings for this term, and they are both at limit point, along with a family of other terms for various arity classes.