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    • Added characterization of κ\kappa-compact objects in λ\lambda-accessible categories.

      diff, v63, current

    • Create a page to discuss the various meanings this prefix has, to avoid confusion. Where possible I have included alternative terminology to use, but there doesn’t always appear to be a good alternative appearing in the literature.

      v1, current

    • Mention the adjoints to the discrete category construction.

      diff, v24, current

    • Added to Hopf monad the Bruguières-Lack-Virelizier definition and some properties.

    • I made some minor improvements to the Properties section of pushout, making it match the similar section in pullback insofar as it can. (It’s a bit tiring to have to look at both these pages to get all the basic properties, so I fixed that, but for properties that hold both for pullbacks and dually for pushouts I’m happy to have all the proofs at pullback - that’s how it works now.)

    • I have touched the formatting at free groupoid. Then I added the statement that the fundamental groups of a free groupoid are free. Also added a pointer to a writeup of the proof.

    • As there had been a change to the entry for Ross Street I gave it a glance. Is there a reason that the second reference is to a paper without Ross as an author?I hesitate to delete it as there may be a hidden reason. (I have edited this discussion entry to remedy the point that Todd and Urs have made below. I also edited the title of this discussion!)

    • I stated this for presheaf categories, but I’m pretty sure that it carries over for any Grothendieck topos.

      Check it out: lawvere interval

    • When pointing somebody to it, I noticed that the entry n-category is in a rather sad state and in particular it used to start out in a rather unhelpful fashion. I have now tried to briefly fix at least the latter problem by expanding and editing the first two sentences a bit. Notably I made sure that a pointer to (∞,n)-category appears early on, for that is a place with more robust information, currently.

    • I have adjusted and expanded wording and formatting in this entry.

      Notice that the definition of the source and target maps that was (and still is) given here differs from that in Dwyer & Kan (1984):

      where Dwyer & Kan’s §3.1(ii) “discards vertices from the right”, the definition that was (and still is) given in the entry seems to want to switch to the convention where vertices are discarded “from the left”.

      With due care this can probably be made an equivalent definition, but as currently stated

      s=(d 1) n+1s = (d_1)^{n+1}

      t=d 0(d 2) nt = d_0(d_2)^n

      this must be wrong in itself: the “d 2d_2” probably wants to be a “d 1d_1”.

      If anyone wants to fix this, feel invited. Otherwise I’ll change this to Dwyer & Kan’s definition.

      diff, v12, current

    • starting an entry on the left adjoint of the homotopy coherent nerve (which seems to have been missing all along)

      v1, current

    • I left a counter-query underneath Zoran’s query at compactly generated space. It may be time for a clean-up of this article; the query boxes have been left dangling and unanswered for quite some time. Either proofs or references to detailed proofs would be welcome.

    • added some details about the ring of power series modeling infinitesimals in fields.


      diff, v26, current

    • created traced monoidal category with a bare minimum

      I would have sworn that we already had an entry on that, but it seems we didn’t. If I somehow missed it , let me know and we need to fix things then.

    • copied from HoTT wiki


      v1, current

    • I noticed only now that the entry bimodule is in bad shape and needs some attention. For the moment I have added here a mentioning of the 2-category of algebras, bimodules and intertwiners and a pointer to the Eilenberg-Watts theorem.

    • Have added to cyclic set a pointer to notes from 1996 by Ieke Moerdijk where the theory classified by the topos of cyclic sets is identified (abstract circles).

      This is an unpublished note, but on request I have now uploaded it to the nLab

      • Ieke Moerdijk, Cyclic sets as a classifying topos, 1996 (pdf)

      I have also added a corresponding brief section to classifying topos.

      By the way, there is an old query box with an exchange between Mike and Zoran at cyclic set. It seems to me that this has been resolved and the query box could be removed (to make the entry read more smoothly). Maybe Mike and/or Zoran could briefly look into this.

    • Added definition of a right module over a monoid

      diff, v9, current

    • started a Properties-section at Lawvere theory with some basic propositions.

      Would be thankful if some experts looked over this.

      Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.

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


      v1, current

    • starting page on left division in modal type theory

      v1, current

    • I created inverse Galois problem. However as it stand this stub does not meet nlab standards since it doesn’t refer to category theory.

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Urs has added Euler integration prompted by Tom’s post at nCafe; I wanted to do that and will contribute soon. I noticed there is no entry integral in nnLab, but it redirects to integration. I personally think that integral as a mathematical object is a slightly more canonical name for a mathematical entry than integration, if the two are not kept separated. Second, the entry is written as an (incomplete) disambiguation entry and with a subdivision into measure approach versus few odd entries. I was taught long time ago by a couple of experts in probability and measure theory that a complete subordination to the concept of integral to a concept of measure is pedagogically harmful, and lacks some important insights. This has also to do with the choice of the title: integration points to a process, and the underlying process may involve measure. Integral is about an object which is usually some sort of functional, or operator, on distributions which are to be acted upon.

      Thus I would like to rename the entry into integral (or to create a separate entry from integration) and make it into a real entry, the list of variants being just a section, unlike in the disambiguation only version. What do you think. Then I would add some real ideas about it.

    • starting page on Darboux integration

      v1, current

    • Created a stub to record a new article and to satisfy a link.

      v1, current

    • creating stub article


      v1, current

    • considerably expanded the entry strict 2-group.

      • Apart from adding an introductory discussion, and expanding the list of examples, in particular by adding that of automorphism 2-groups ...

      • ... I in particular give the detailed translation prescription for how to encode a 2-group by a crossed module at In terms of crossed modules

      This is to eventually serve as a supplement to the discussion at nonabelian group cohomology. So I spent some energy on disentangling the four different (though isomorphic) ways a crossed module gives rise to a 2-group (following my article with David Roberts).

    • 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.

    • The statement had been laying dormant here for about a dozen years, without a proof. I’ve finally put some meat on the bones.

      diff, v2, current

    • copying text from HoTT wiki


      v1, current

    • I’ve been adding a considerable amount of detail to relational beta-module. Not quite finished, but a lot of former ellipses have been filled in, and technical results proved from scratch.

      If anyone knows this material, I’d enjoy hearing of any proposed simplifications. My local university library does not have the Springer Lecture Notes where Barr first wrote his article on relational beta-modules, and it’s hard finding detailed material at this ground level on the internet, so this represents pretty much what I’ve been able to work out by myself. (And it might read that way.)

    • I tried to prettify the entry topological space a bit more:

      • made an attempt at adding an Idea-section (feel free to work on that, it’s just a quick idea motivated more from the desire to have such a section at all than from an attempt to do it any justice).

      • collected the three Definition-sections to subsections of a single Definition-section

      • polished and expanded the Standard definition section.