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    • Anonymous “helpfully” changed the statement

      A matrix is a list of lists.

      to

      A matrix is a function M:[n]×[m]→XM:[n]\times[m]\rightarrow X from the Cartesian product [n]×[m][n]\times[m] to a set XX.

      which I have reverted back.

      diff, v12, current

    • for ease of linking, I gave this its own little entry

      v1, current

    • gave this statement its own entry, as it is being referenced or used in a variety of other entries. Also spelled out a proof. Not a short one but, hopefully, a conceptual one.

      v1, current

    • I have added the actual general definition of the Cech groupoid as presheaf of groupoids, and headlined the definition previously offered here as “Idea”. Then I added detailed statement and proof, that the Cech-groupoid co-represents sets of matching families for set-valued presheaves (now this prop.)

      diff, v7, current

    • This entry is currently undecided as to whether “full subcategory” inclusion requires the functor to be an injection on objects. It begins by pointing to subcategory which does require this, but before long it speaks about fully faitful functors being full subcategory inclusions.

      This will be confusing to newcomers. There should be at least some comments about invariance under equivalence of categories.

      Ah, now I see that at subcategory there is such a discussion (here). Hm, there is some room for cleaning-up here.

      diff, v10, current

    • Created page, with a brief definition of the rules, and a remark that the naive formula for cofree comonoids always satisfies the laws of the soft exponential (is this well-known?)

      v1, current

    • “small site” used to redirect to “little site”. Despite the warning there, this doesn’t seem helpful, and so I created a little disambiguation entry

      v1, current

    • I have expanded a little at sifted category: added the example of the reflexive-coequalizer diagram, added the counter-examples of the non-reflexive coequalizer diagram, added a references.

    • Page created, but author did not leave any comments.

      v1, current

    • some minimum, for ease of hyperlinking

      v1, current

    • fixed numdam link to DeligneMumford69

      apparently, numdam changed their link scheme… are any other links to numdam on the nlab broken? maybe someone with search-fu and/or bot writing skills wants to check/repair that.

      Konrad Voelkel

      diff, v4, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Work-up of an article that explains “Scott’s trick” for forming quotients of large classes as classes.

      v1, current

    • Page created, but author did not leave any comments.

      Alexander Schmeding

      v1, current

    • The inductive tensor product is the analogue of the projective tensor product where we have a universal property wrt separately continuous maps. For Fréchet spaces they agree.

      v1, current

    • I have added to locally convex topological vector space the standard alternative characterization of continuity of linear functionals by a bound for one of the seminorms: here

      (proof and/or more canonical reference should still be added).

    • added a reference and some comments about the relation between Lie groupoids and their groups of bisections

      A. Schmeding

      diff, v7, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Non-trivial edit made, but author did not leave any comments.

      diff, v14, current

    • Added Todd's definition of *-quantale to quantale. Is there anything about enrichment in such things that's worth adding?

    • created an extemely stubby stub Weiss topology, just to record pointer to that cool fact which Dmitri Pavlov advertised on MO (here).

      I have no time to expand on the entry right now. But maybe somebody else here does? Would be worthwhile.

    • Add some notes about getting twelf to work on modern Ubuntu

      diff, v3, current

    • Looking back at an old Café thread, I see Neil Strickland telling us about Baas-Sullivan theory.

      Various comments:

      1) Baas-Sullivan theory allows you to start with a cobordism spectrum R and introduce singularities to construct R-module spectra that can be thought of as R/(x1,…,xn), where xi ∈ π*R.

      2) This is computationally tractable when the elements xi form a regular sequence. You can construct connective Morava K-theories from complex cobordism this way, for example. You can also get ordinary homology, as the cobordism theory of complexes that are allowed arbitrary singularities of codimension at least two.

      3) The original Baas-Sullivan framework is quite technical, and combinatorially complex. It is now easier to use the framework developed in the book by Elmendorf, Kriz, Mandell and May.

      4) This procedure always gives R-modules, so if you start with MU (= complex cobordism) or MSO or MO, you will always end up with something complex orientable. In particular, you cannot get tmf or KO or the sphere spectrum from MU.

      5) You can get more things if you do cobordism of manifolds with extra structure, such as a spin bundle or framing, for example. It is probably possible to get kO from MSpin. It might even be possible to get tmf from MString.

      6) There is a theorem that I think appears in an old book by Buoncristiano, Rourke and Sanderson, showing that any generalised homology theory is a cobordism theory of manifolds with some kind of extra structure and singularities. I don’t think that they were able to given any nonobvious concrete examples other than ordinary homology, and I don’t think that anyone else has managed to go anywhere with this theory. But perhaps it would be worth taking another look.

      Let’s see if any passing expert can help with an entry.

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Is there a reason the article on abstract stone duality uses the term ∞\infty-calculus when linking to λ\lambda calculus? Looks like it’s been there since the original page by David Corfield. I was going to just change it to λ\lambda, but it seems intentional.

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Started MacNeille completion. Is there not a snappy category theoretic way of describing the construction?

    • I may as well start an entry focusing, since after mentioning it here I did at least come across some references.

      Hopefully a kind passing type theorist will write something substantial.

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Some bare minimum for the moment. Plus pointers to how this is the setup for geometric engineering of the 6d (2,0)(2,0)-superconformal QFT on both sides.

      v1, current

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