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    • 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.

    • 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.
    • 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…)