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    • Added the proof that every positive operator is self-adjoint.
    • For my first contribution to nLab, I've typed up my notes on effect algebras, with the definitions of a generalized effect algebra and morphism of effect algebras. The proofs here are more basic than most that I've seen on the wiki, but I've decided to include them in the spirit of this being a public lab book.
    • Back in the days I had made several web postings on the “FRS formalism” and how it may be understood as rigorously implementing “holography” in the form of CS/WZW-correspondence. Ever since the nLab came into being there was a stub entry FFRS-formalism which collected some (not all) of these links.

      Now I got a question on how it works. (As a student one cannot imagine yet that communication in academia/maths often has latency periods of several years….) While I have absolutely no time for this now, this afternoon I went and expanded that stub entry a bit more (and maybe it’s at least good for my own sanity in these days). Also renamed it to something more suggestive, now it is titled

      There is still plenty and plenty of room to expand further (urgent would be to mention the tensor produc of the MTC with its dual, which currently the entry is glossing over), but I am out of time now.

    • I have added to SimpSet a list of a few properties of the internal logic of the 1-topos of simplicial sets.

    • Hello all,
      I liked very much the nLab-entry "well-founded relation": concise and informative.
      Do you think "lexicographic order" may be included in the section Examples as another, practically relevant example of well-founded relation?
      If yes, I would be very grateful if somebody could do that (I am not an expert).

      Best regards from Germany
    • Hello,
      I have just created a page on C*-correspondences (http://ncatlab.org/nlab/show/C-star-correspondence). I will add a few stuff about the weak 2-category of C*-algebras built upon those later.
    • An entry which defines both the local category and the local Grothendieck category, two notions which generalize the notion of a category of modules over a commutative local ring.

    • Old discussion at star-autonomous category, which I think was addressed in the entry, and which I’m now moving here:

      +–{: .query} Mike: Can someone fill in some examples of **-autonomous categories that are not compact closed?

      Finn: Blute and Scott in ’Category theory for linear logicians’ (from here) give an example: reflexive topological vector spaces where the topologies are ’linear’, i.e. Hausdorff and with 0 having a neighbourhood basis of open linear subspaces; ’reflexive’ meaning that the map d Vd_V as above is an isomorphism. It seems this category is **-autonomous but not compact. I don’t know enough topology to make much sense of it, though.

      Todd: Finn, I expect that example is in Barr’s book, which would then probably have a lot of details. But I must admit I have not studied that book carefully. Also, the Chu construction was first given as an appendix to that book.

      John: I get the impression that a lot of really important examples of **-autonomous categories — important for logicians, anyway — are of a more ’syntactical’ nature, i.e., defined by generators and relations. =–

    • I have started something at computability.

      Mainly I was after putting some terms in organized context. That has now become

      which I have included under “Related concepts” in the relevant entries.

    • created a minimum at computable real number, for the moment just so as to record the references with section numbers as given there.

    • just in case you are watching the logs and are wondering:

      I think we should have another “floating table of contents” for collecting the topic cluster

      • Constructivism, Realizability, Computability

      so I am starting one at constructivism - contents and am including it into relevant entries.

      But right now there is nothing much there yet. This is going to be expanded.

    • Created a brief entry transfer context in order to record an observation by Haugseng.

      He defines a transfer context to be a linear homotopy-type theory aka Wirthmüller context in which not only f !f_! but also f *f_\ast satisfies its projection formula. Then he observes that a natural Umkehr map that may be built with this projection formula is (the abstract generalization of) the Becker-Gottlieb transfer.

      (Have briefly cross-linked with these related entries.)

      Thanks to Thomas Nikolaus for being reminded of Haugseng’s work when Joost Nuiten and me talked about something closely related as ESI yesterday.

    • I added some basic definitions to stability in model theory. No attempt yet to motivate them.

      Some of the logic entries seem to be in a slight state of neglect, e.g., theory. I might want to get in there sometime soon, but anyone should please feel free to precede me.

    • for some reason it seems we never had an entry compactly generated (infinity,1)-category (and out of all sections listed at HTT just 5.5.7 had been missing for some reason which is a mystery to me now).

      I gave it a minimum of content. But this alerts one that there is a distinction being made here which we don’t have in the corresponding 1-categorical entries.

    • I’ve been adding material to Polish space, and plan on adding more (mostly in view of model-theoretic considerations).

    • created a stub for completion monad.

      In the course of doing so I found it unfortunate that the link constructive analysis simply redirected to analysis, a page from which the constructive formulation and the point of it was hardly to be extracted. So I have split off constructive analysis right now. But except for a sentence pointing back to the completion monad, it just contains for the moment the list of references that we already had.

    • cretaed a brief entry K-motive in order to record a cool statement somewhat hidden in an article by Tabuada froma year back. Thanks a lot for Adeel Khan Yusufzai for pointing this out!

    • I changed the entry Cahiers to state that the free back issues are only available up until 2008, rather than with a two-year moving wall, as one can check. Also, I notice that the journal home page and the TAC mirror of the contents is a year behind (only info up till the end of 2012). Does anyone know anything about this?

    • I was disappointed to discover that Boman's theorem doesn't work as one would like for C kC^k functions with 0<k<0 \lt k \lt \infty. So I wrote up something about it. (This is all in Boman's 1967 paper; he covered everything in 20 freely accessible pages!)

    • I gave Todd’s note A string diagram calculus for predicate logic a category:reference entry, turned the ps-file into a pdf and linked to it there, and then added pointers to this from relevant entries, such as hyperdoctrine and indexed monoidal categories, each going along with pointers to Ponto-Shulman.

      This in an attempt to make more visible all the little pointers that are (or were now) hidden behind “here”-s at string diagram. Eventually that entry should be a bit clearer about what all that stuff is that it secretly subsumes.

    • Todd had filled in some text at Trimble rewiring. I have added a few more hyperlinks now and a floating TOC.

      Todd, when you have another minute, could you say a bit more specifically what a Trimble rewiring does? Which kinds of diagrams are rewired how, and what’s the deal?

    • the nLab was lacking an entry invertible object. I have started a minimum there, just so as to satisfy links for the moment.

    • stub for coherent (infinity,1)-topos, just to record the pointers to the DAGs.

      (Thanks to Marc Hoyois for pointing out the hidden proposition in DAG XIII…)

    • The link bilimit used to redirect to 2-limit. With this the reader following this might miss the sense of biproducts.

      I have now removed the redirects and instead made bilimit a category:disambiguation-page. Hopkins-Lurie suggest to speak of “ambidextrous diagrams” (spaces) instead, which is maybe an option out of the terminology clash.

      So finally at ambidextrous adjunction I have added the case of coinciding limits and colimits as an example.

    • created finite homotopy type, just for completeness.

      This just a distraction when I saw that it was missing,while I was really going to create an entry on truncated homotopy types with finite homotopy groups.

      The main problem about them is that nobody agrees on how to call them ;-)

      In groupoid cardinality they have been called “tame”, some call them π\pi-finite,I suppose, and homological algebra suggests “of finite type”, which in itself is good, however rather badly goes together with the crucially different “finite homotopy type”.

    • The link to Joyal’s Catlab discussion at Cisinski model structure leads to a page on his Lab at which the main link points to a non-existent pdf document at Paris 13. We have the correct link at Cisinski model structure, namely to his Toulouse address (http://www.math.univ-toulouse.fr/~dcisinsk/ast.pdf). What is the best way to fix this? I do not seem to have access to Joyal’s Lab to be able to edit that.