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    • added to (infinity,1)-operad the definition/proposition of the model structure for the category of (oo,1)-categories of operations here

    • I added to vertical categorification the comments that I'd made at MathOverflow, as Urs has requested. I'm not sure that I'm happy with where I put them and how I labelled them, but maybe it's better if other people judge that.

    • Added some more to the ongoing discussion about composition at evil.

      (fixed)
    • I'd like to add the following "shape" to http://ncatlab.org/nlab/show/limit#types_of_shapes_of_limit_cones_17 :

      The limit of the identity functor Id: C --> C is the initial object of C (it it exists).
    • I've added the latest, almost complete, draft of my thesis to my personal web - go via David Roberts. Comments on introduction are welcome, if you feel so inclined. Just put them on David Roberts.

      On a related note, is it quite legitimate to post updates on personal webs here? (Now that I've already done it)

      David Roberts
    • Edited the page category theory. Mostly about that certain presheaves are the same as categories and the long discussion at the end with an idea how to solve my problem about CW-complexes. Removed precursors link since there is nothing about them in nLab. This new logging is a bit confusing and harder to read.

      -Rafael
    • Created universal algebra in a monoidal category

      In the lab book metaphor, this page is some jottings of stuff that I'm pretty sure must be out there (as it's a fairly obvious thing to do) but have no idea of what it's called (hedgehogs, perhaps?). So I'd be grateful if someone strong in the ways of Lawvere theories could stop by and help me out.

      (Plus I had to make up the notation and terminology as I went along so that's all horrible)

      Hopefully the big box at the top of the page makes this clear!

    • I apologize in case this discussion is already open and I have been unable to find it.

      There is something I am unable to undrstand in the definition of extended TQFT as on the nLab page http://ncatlab.org/nlab/show/extended+topological+quantum+field+theory

      Namely, it seems to me that the recursive definition should rather end with "smooth compact oriented (n-m+1)-manifolds to R-linear (m?2)-categories"
    • One of these has started (or continued) a conversation at the bottom of graph.

    • I'm guessing that ferrim is spam. If no-one says anything to the contrary within 24hrs then I'll add it to the spam category.

      If it is spam, it's either a random spambot post or it's someone testing to see how vigilant we are. If the latter, as there's no content then they may simply test to see if the link stays active. In which case, our previous "policy" of blanking the content won't send the right signal here (especially as there's no content to blank). Is there any objection to renaming spam entries? Say, as 'spam (original title)' (or whatever the allowable punctuation characters are)?

    • In entry groupoid object in an (infinity,1)-category there is a passage

      "it is the generalization of Stasheff H-space from Top to more general ?-stack (?,1)-topoi: an object that comes equipped with an associative and invertible monoid structure, up to coherent homotopy"

      I repeat what I documented in earlier discussion on H-space: H-spaces are widely used terminology since 1950, thus before Stasheff work which of course is an important work on coherencies for them. So it is likely improper to say Stasheff H-space...Stasheff has REFINEMENTS of H-spaces, namely $A_n$-spaces and the group-like case is A infty spaces.

    • Somebody named ‘Harry’ has a comment at evil. Presumably it is of interest to Mike and me.

    • Added topological cube to cube, and removed some JA-esque redirects from terms like succubi and so forth.

      David Roberts
    • I see Mike's 1-category equipment

      May I vote for the following: we should "play Bourbaki" and correct the naming mistake made here. The obvious name one should use is "pro-morphism structure".

      We equip a category with pro-morphisms.

      We equip a category with a pro-morphism structure.

      Or, if you insist,

      We equip a category with pro-arrows.

      We equip a category with a pro-arrow structure.

      But the day will come when you want a pro-2-morphism structure. And then one will regret having used "arrow" instead of "morphism".

      I mean, compared to issues like "presentable" versus "locally presentable", this idea of saying just "equipment" is a bit drastic, to my mind.

    • I'd like to write something about a Quillen equivalence, if any, between model structures on

      • n-connected pointed spaces

      • grouplike E-n spaces .

      With the equivalence given by forming n-fold look spaces.

      But I need more input. I found a nice discussion of a model structure on n-connected pointed spaces in A closed model category on (n-1)-connected spaces. I suppose there is a standard model structure on E-k algebras in Top. Is a Quilen equivalence described anywhere?

    • I added to directed colimit the  \kappa -directed version, for some regular cardinal  \kappa .

      We should maybe also add to directed set the  \kappa -directed version. What we currently descrribe there is just the  \kappa = \aleph_0 -directed version.

      Accordingly then I also added to compact object the definition of the variant of  \kappa -compact objects.

      At small object previously it mentioned " \kappa-filtered colimits". I now made that read " \kappa-directed colimits".

      I hope that's right. If not, do we need to beware of the differene?

    • I created biactegory following my 2006 work and being prompted by overlapping work of a student of Nikshych which appeared on the arXiv today.
      • created entry for Dan Freed and added some links to articles by him here and there

      • expanded the discussion of face maps at dendroidal set a little

    • I did a wee bit of editing of "Dold-Kan correspondence", trying to incorporate Kathryn Hess' wisdom into this page. A lot of this stuff involves the monoidal aspects of the Dold-Kan correspondence, but I was too lazy to edit the separate page "monoidal Dold-Kan correspondence". I would ideally like that page to focus equal attention to chain complexes as it now does to cochain complexes!