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    • 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 0→A→G^ i→G→00 \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:

      A⊕A → A⊕A ↓ ↓ Δ *(G^ 1⊕G^ 2) → G^ 1⊕G^ 2 ↓ ↓ G →Δ G G⊕G \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:

      A⊕A →+ A ↓ ↓ Δ *(G^ 1⊕G^ 2) → + *Δ *(G^ 1⊕G^ 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 X→im n(f)X \to im_n(f) induces an epimorphism on connected components”

      to

      “The map X→im n(f)X \to im_n(f) induces an epimorphism on homotopy groups in degree n−1n-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.

    • I saw that one of the classical arity classes didn't have a name, so I named it ‘subunary’.

    • I just deleted the query

      Did you do these edits attributed to ’Ronald null Brown’? —Toby

      at Ronnie Brown.

    • added an entry for the Kan Thurston Theorem.
      http://ncatlab.org/nlab/show/Kan-Thurston+Theorem

    • A few grad students and I are starting a reading group on the Firewall problem and related aspects, so I’ve created a page in the nLab with a bunch of relevant papers:

      (not yet a complete list.)

      The goal will be to develop the page into a introduction to the problem, and the resolutions proposed, etc.

    • you all knew it was about to happen, and now it did: I have created a table-of-contents page for inclusion as “floating TOC” in the relevant entries:

    • added to limit in a quasi-category (in the Properties-section) more details on how the definition in terms of over over-categories is equivalent to the one in terms of homs. But still not done.

    • added the definition of relative (infinity,1)-limit, because I need to point to it from elsewhere.

      (Somehow the cache bug, or a new version of it kicked in, and there is now also relative (∞,1)-limit, which I won’t try to fight with just right now…)

    • Someone (probably in Gottingen) created a slideshow page. I renamed it Slideshow sandbox and removed its contents which were

      www.math.columbia.edu/~woit/notes16.pdf

      That was the old name as well.

    • Euclid (Εὐκλείδης) was the ancient Greek version of Bourbaki.

    • Urs created submersion and I added a little more. Still a bit stubby, though.

    • I have added the Nadler’s today’s paper at Waldhausen S-construction. It would perhaps make sense to quote it in some more entries.

    • Someone has made a change to the page on Aleksandr Aleksandrov, but there are some characters in the Cyrillic form of his name that are not coming out. Does anyone know how to fix this?

    • am starting to make some basic notes on Gysin/Umkehr/pushforward maps in KK-theory, currently in fiber integration in the section In KK-theory. But still with some gaps.

    • started stub for Chow group

      hoping I got this right...

    • I created the page

      h-topology

      (just a stub right now).

    • Started smooth loop space, initially just a stub. Partly to contain some bits of general theory relating to which smooth paths do I use (davidroberts) and partly to start transferring some notes on the differential topology of loop spaces over to the nLab.

      In looking for somewhere to graft it on to the current nLab tree, I encountered loop space object. It seemed to me that the smooth loop space is not a loop space object, so I commented as such (thus also creating the link to smooth loop space which was my real intent). Someone who knows these things better than I do should check this.

    • created product law, since I wanted to be able to link to it…

    • Created the page unbounded topos, and some links at topos and bounded geometric morphism.

      I’m interested in the generalisation of the construction of the unbounded topos Gl(F)Gl(F) to the general case of an inaccessible comonad GG on a bounded topos (which wlog we might as well take to be SetSet EDIT: NO, LET’S NOT). In essence, why is it unbounded? Also, what nice properties can we claim of the category of coalgebras for GG, given information about GG.

      Note also, the paper HOW LARGE ARE LEFT EXACT FUNCTORS? in TAC in 2001 seems to claim something a little stronger than Johnstone does in the Elephant, and recounted at topos, namely that the existence of lex endofunctors of set is independent of ZFC (they say something more general, but it covers this case). This is mostly a note to myself, but if others feel like looking, that would be good too.

    • You may have seen in “Recently revised” that I had edited 11-dimensional supergravity in the last days. I wanted to start a section there on the details of the action functional. But after adding some formulas, I ran out of time and just left an “under construction”-warning.

      The reason I ran out of time is that I had to first write related things with higher priority into an article we are currently preparing:

      Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory.

      Later when the dust has settled and I have more leisure, I’ll try to take care of the nnLab’s 11d sugra article again.

    • wrote something at cosmic string and by copy-and-pasting-and-changing-the-degrees added something similar to domain wall and monopole. Needs a bit more polishing, maybe.

      I am really working on writing out an abstract re-formulation of this classical theory in terms of extended TQFT with defects, but not done with that yet (and will probably be interrupted again before finishing it).

    • There used to be a warning at infinity-Lie algebra cohomology about whether or not a certain functor needs to be regarded as a derived functor in order to get the correct homotopy-theoretic interpretation of oo-Lie algebroid extensions. I think I have now spelled out at synthetic differential infinity-groupoid the required details and so I replaced that warning with a pointer to a section in that latter entry.

      All this can do with a good bit more polishing. I’ll see what I can do eventually.

    • I added a link to EoM at Lie’s three theorems, where there is a statement of the first theorem - we just had the slightly disparaging sentence

      …is today regarded as lacking a good notion of differentiable manifold.

    • stub for Tamagawa number, for the moment just so as to record the article relating it to YM theory.

    • I archive here the query box from homological algebra and finite element method.

      Eric: The appearance of homological algebra in finite element methods goes back a lot earlier than Arnold. It is covered somewhat extensively in Robert Kotiuga’s (who happened to be John Baez’s dorm room mate at MIT) PhD dissertation:

      • Kotiuga, P.R., Hodge Decompositions and Computational Electromagnetics, Ph.D. Thesis, McGill University, Montreal, Canada, 1985

      I don’t think Robert would claim to be the earliest.

      Then you can go back to 1976 with Józef Dodziuk’s classic paper:

      • Finite difference approach to the Hodge theory of harmonic forms, Amer. J. Math., 98 (1976), 79-104.

      Zoran: Surely, it is emphasised that the numerous precursors exist in the Bulletin survey of Douglas Arnold et al. quoted below. But it was not in any sense systematic till rather recently. One could expand on the history…

      I have today posted a question to MathOverflow on recent-fundamental-new-directions-in-pdes.

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