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    • Began stub for Tambara functor. Neil Strickland’s, Tambara Functors, arXiv:1205.2516 seems to be a good reference.

      Seems like it’s very much to do with pullpush through polynomial functors, if you look around p. 23.

      I would try to say what the idea is, but have to dash.

    • the page action is also a mess. I have added a pointer to the somewhat more comprehensive module and am hereby moving the following discussion box from there to here:

      [ begin forwarded discussion ]

      +–{.query} I am wondering if we will need the notion of action which works in categories with product, i.e. G×X→XG\times X\to X and so on. There is also an action of one Lie algebra on another (for instance in some definitions of crossed module of Lie algebra, where AutAut is replaced by the Lie algebra of derivations. (a similar situation would seem to exist in various other categories where action is needed in a slightly wider context. I think most would be covered by an enriched setting but I am not sure.) Thoughts please.Tim

      Yes, I think certainly all those types of action should eventually be described somewhere, possibly on this page. -Mike

      Tim: I have added some of this above. There should be mention of actions of a monoid in a monoidal category on other objects, perhaps.

      Mac Lane, VII.4, only requires a monoidal category to define actions. – Uday =–

      [ end forwarded discussion ]

    • I added a bit to category of simplices, including the fact that the category of nondegenerate simplices is final and thus colimits can be computed using only that, and that the nerve of the category of simplices itself is colimit-preserving.

    • Changes made only to the Universal property of the 2-category of spans section. The citations by Urs lead to another citation which, in turn, leads to another citation. With a little effort, I tracked down the a full copy of said universal property, I’ve replicated it here, added the citation used, although I left the previous citations there for convenience; a more experienced editor can remove those if they would like.

      I would like to note that the author whose work I have referenced, Hermida, also notes: “[this universal property] is folklore although we know no references for it.”

      Please make any corrections needed and clean up the language here; this is a fairly direct copy of what is written, but I imagine somebody with more knowledge of all the language used here can rewrite this universal property stuff in a cleaner way.

      Thanks!

      Anonymous

      diff, v57, current

    • Create a stub. I will expand the list shortly.

      v1, current

    • starting a dedicated entry for the category of vector bundles with homomorphisms allowed to cover non-trivial base maps (while previously we only had VectBund(B) for fixed base BB).

      For the moment the main point is to record the interesting cartesian- and tensor-monoidal structure (now here)

      v1, current

    • I will brush-up the entry homotopy hypothesis. But not right now, right now I have to run and do something else. But here is some leftover discussion that was sitting there, and which I have now removed from the entry and reproduce here, in order that we go and use it to make the entry better, but not clutter it up.

      (continued in next comment)

    • a category:reference-entry (“FGA” used to redirect to EGA)

      v1, current

    • starting a stub. Nothing here yet, but need to save.

      v1, current

    • At crossed module it seems we are missing what i think should be the prototypical example: the relative second homotopy group π 2(X,A)\pi_2(X,A) together with the bundary map δ:π 2(X,A)→π 1(A)\delta:\pi_2(X,A)\to \pi_1(A) and the π 1(A)\pi_1(A)-action on π 2(X,A)\pi_2(X,A). As someone confirms this example is correct I’ll add it to crossed module.

    • Changed typo’d “pyschoaccoustics” to correct “psychoacoustics”.

      Anonymous

      diff, v16, current

    • starting something – not done yet

      v1, current

    • I added a reference to a paper of mine

      Amnon Yekutieli

      diff, v48, current

    • Adjust the idea section. Representability is a property of a multicategory, rather than a construction on monoidal categories.

      diff, v13, current

    • This alone would not be an improvement over point particle versions of quantum gravity except that it is possible to define a perturbative expansion of string theory around a fixed, classical background space-time that is finite and anomaly free at 1-loop

    • I reorganized linearly distributive category by moving the long block of history down to the bottom, adding an “Idea” section and a description of how **-autonomous categories give rise to linearly distributive ones and linearly distributive ones give rise to polycategories. I also cross-linked the page better with polycategory and star-autonomous category.

    • Mentioned a characterisation of exponentiable multicategories.

      diff, v33, current

    • A bare minimum, for the moment just in order to make the link work at all.

      (And leaving much room for disambiguation.)

      v1, current

    • added pointer to:

      removed the following ancient query box discussion:

      +–{.query} Left I could understand, but right? —Toby

      The way I rewrote it explains it. It is unfortunate that the Eilenberg-Watts theorem treated in Bass was using only right adjoint functors so later they dropped word right. – Zoran

      Thanks. —Toby =–

      diff, v12, current

    • I have added at HomePage in the section Discussion a new sentence with a new link:

      If you do contribute to the nLab, you are strongly encouraged to similarly drop a short note there about what you have done – or maybe just about what you plan to do or even what you would like others to do. See Welcome to the nForum (nlabmeta) for more information.

      I had completly forgotton about that page Welcome to the nForum (nlabmeta). I re-doscivered it only after my recent related comment here.

    • added missing publication data to some references, and added this new reference:

      • D. Melnikov, A. Mironov, S. Mironov, A. Morozov, An. Morozov, A modular functor which is universal for quantum computation, Nucl. Phys. B926 (2018) 491-508 (arXiv:1703.00431)

      diff, v5, current

    • just for completeness, since I want to be able to link to this term

      v1, current

    • Describing the arrangements which have been made for funding of the nLab in collaboration with the Topos Institute. The page, linked to from the home page, is intended to be fairly general; specific requests for donations can be made elsewhere.

      v1, current

    • Added a couple of recent references in condensed matter physics.

      diff, v12, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • starting something on the concept introduced in

      • Sergei O. Ivanov, Roman Mikhailov: A higher limit approach to homology theories, Journal of Pure and Applied Algebra 219 6 (2015) 1915-1939 [arXiv:1309.4920, doi:10.1016/j.jpaa.2014.07.016]

      • Sergei O. Ivanov, Roman Mikhailov: Higher limits, homology theories and fr\mathbf{fr}-codes, in: Combinatorial and Toric Homotopy, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore (2017) 229-261 [arXiv:1510.09044, doi:10.1142/9789813226579_0004]

      but for the moment there is little more than these references

      v1, current

    • Re-instantiating the entry announced here, with slight change to title and text.

      v1, current

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