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    • Since the page geometry of physics – categories and toposes did not save anymore, due to rendering timeouts caused by its size, I have to decompose it, hereby, into sub-pages that are saved and then re-!included separately.

      With our new announcement system this means, for better or worse, that I will now have to “announce” these subsections separately. Please bear with me.

      v1, current

    • Since the page geometry of physics – categories and toposes did not save anymore, due to rendering timeouts caused by its size, I have to decompose it, hereby, into sub-pages that are saved and then re-!included separately.

      With our new announcement system this means, for better or worse, that I will now have to “announce” these subsections separately. Please bear with me.

      v1, current

    • Since the page geometry of physics – categories and toposes did not save anymore, due to rendering timeouts caused by its size, I have to decompose it, hereby, into sub-pages that are saved and then re-!included separately.

      With our new announcement system this means, for better or worse, that I will now have to “announce” these subsections separately. Please bear with me.

      v1, current

    • Although referred to in a couple of place, it seems we had no entry for spatial topos, so I’ve made a start.

    • Since I got questions from the audience (here) why I defined (pre-)sheaves on a site, instead of on a topological space “as in the textbooks”, I created this little entry with some basic pointers, which may complement the entry localic topos for the newbie. Could of course be expanded a lot…

      v1, current

    • I added exposition (here) of how floor and ceiling are the left and right adjoints to the full embedding of the integers into the real numbers

      diff, v3, current

    • minimum category:people entry for the purpose of hyperlinking refernces

      v1, current

    • In the article cocylinder one reads at the bottom:

      George Whitehead, Elements of homotopy theory
      (This uses the terminology mapping path space.)
      

      (This was added in revision 3 by Mike Shulman.)

      However, I was unable to find any occurrence of this terminology in Whitehead’s book.

      Indeed, looking at the table on page 141 below Theorem 6.22, we see that Whitehead refers to the dual construction as the mapping cylinder I_f, whereas the original construction is denoted by I^f, but there is no name attached to it.

      Furthermore, on page 43 below Theorem 7.31 one reads:

      The process of replacing the map f: X→Y by the homotopically equivalent fibration p : I^f→Y
      is, in some sense, analogous to that of replacing f by the inclusion map of X into the mapping cylinder of f;
      the latter is a cofibration, rather than a fibration.
      Pursuing this analogy further, we may consider the fibre T^f of p over a designated point of Y.
      We shall call T^f the mapping fibre of f (resisting firmly the temptation to call I^f and T^f the mapping cocylinder and cocone of f!).
      
    • I have expanded norm a bit.

    • Cleaned up formatting, adding toc and related concepts

      diff, v4, current

    • Created algebraic theories in functional analysis. I've recently learnt about this connection and would like to learn more so I've created this page as a place to record my (and anyone else's) findings on this. I probably won't get round to doing much before the new year, though.

    • 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.

    • did a little bit of reorganization. Removed one layer of subn-sections, moved the lead-in paragraphs to before the table of contents, added cross-links to geometry of physics – categories and toposes at the point where the concept of categories appears.

      diff, v3, current

    • 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.