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    • In line with the “pages named after theorems” philosophy, I’ve created toposes are extensive, including in particular the (somewhat hard to track down) constructive proof that a cocomplete elementary topos is infinitary extensive.

    • I finally gave spectral super-scheme an entry, briefly stating the idea.

      This goes back to the observation highlighted in Rezk 09, section 2. There is some further support for the idea that a good definition of supergeometry in the spectrally derived/E E_\infty context is nothing but E E_\infty-geometry over even periodic ring spectra. I might add some of them later.

      Thanks to Charles Rezk for discussion (already a while back).

    • I added some results and references at Calkin algebra after I noticed that Zoran had added some comments about set-theoretic axioms leading to different properties. In particular the outer automorphism algebra of the Calkin algebra is trivial or not, depending on whether one has CH, or something that violates CH, Todocevic’s Axiom.

    • Created a page for DLO, the (first-order) theory of (,<)(\mathbb{Q},&lt;). Made some notes about model-theoretic properties, Cantor’s theorem that all countable models of the theory are isomorphic, and also remarked (based on an exercise from Mac Lane and Moerdijk) that the subobject classifier for the topos Set (,<)\mathbf{Set}^{(\mathbb{Q},&lt;)} can be naturally identified with the Dedekind cuts on \mathbb{Q}.

    • Created Fraïssé limit.

      (I was pleasantly surprised to see @David_Corfield had posted about the these things a while ago for the n-Category Cafe.)

      Mentioned a neat result of Olivia Caramello’s that omega-categorical structures presentable as Fraisse limits are determined by their automorphism groups GG with the topology of pointwise convergence in a very nice way: their classifying toposes are precisely the toposes of continuous GG-sets.

      To fill in a grey link, I also created an entry for the countable random graph.

    • created model structure on dg-comodules, just so as to record a pointer to Positelski 11, theorem 8.2.

      Regarding the dg-comodules which are injective as graded comodules over the underlying graded cocommutative co-algebra: Suppose the latter is co-free and the ground ring is a field. Is it then true that all injective comodules over it are cofree? Because this would seem to be a dual version of the Quillen-Suslin theorem?

    • I changed ‘SEAR is a dependent type theory’ at SEAR to ‘SEAR is a dependently typed theory’. A type theory is a general theory of types, including lots of type formation rules; SEAR is a theory of sets written in a dependently typed first-order logic with very few type formation rules.

      But I still linked to dependent type theory, since we don't seem to have good material on using type systems with first-order logic.

    • created a stub entry for comodule spectrum, for the moment just so as to briefly record the result by Hess-Shipley 14 that comodule spectra over suspension spectra of connected spaces XX are equivalently parameterized spectra over XX. Added that reference also to A-theory. Needs to be expanded further.

      (Thanks to Charles Rezk for the pointer.)

    • originating from another thread (here):

      jesse kindly created ultraroot. I have added some more hyperlinks to some more of the keywords.

    • for the purposes of having direct links to it, I gave a side-remark at stable Dold-Kan correspondence its own page: rational stable homotopy theory, recording the equivalence

      (H)ModSpectraCh () (H \mathbb{Q}) ModSpectra \;\simeq\; Ch_\bullet(\mathbb{Q})

      I also added the claim that under this identification and that of classical rational homotopy theory then the derived version of the free-forgetful adjunction

      (dgcAlg 2) /[0]Uker(ε ())SymcnCh () (dgcAlg^{\geq 2}_{\mathbb{Q}})_{/\mathbb{Q}[0]} \underoverset {\underset{U \circ ker(\epsilon_{(-)})}{\longrightarrow}} {\overset{Sym \circ cn}{\longleftarrow}} {\bot} Ch^{\bullet}(\mathbb{Q})

      models the stabilization adjunction (Σ Ω )(\Sigma^\infty \dashv \Omega^\infty). But I haven’t type the proof into the entry yet.

    • I gave simplicial Lawvere theory an entry, stating Reedy’s result on the existence of the simplicial model structure of simplicial algebras over a simplicial Lawvere theory

    • almost missed that meanwhile we have an entry pullback-power. So I added more redirects and expanded a little.

    • The entry minimal fibration used to be just a link-list for disambiguating the various versions. I have now given it some text in an Idea-section and a pointer to Roig 93 where the concept is considered in generality.

    • James Dolan gave a series of talks on algebraic geometry for category theorists at John Baez's seminar, but it seems that the links on the nLab page no longer work. Does anyone know if the videos have been uploaded elsewhere?

      https://ncatlab.org/jamesdolan/published/Algebraic+Geometry
    • Included Lie integration of finite-dimensional real Lie algebras as an example of a coreflective subcategory. The coreflector is Lie differentiation.
    • I added linear logic and type theory (homotopy type theory was already there) to true, which I renamed to truth to make it a noun (although something like true proposition, which I made a redirect, could also work). I then edited false (now falsehood) to include everything in truth.

    • I wanted to understand Borel's Theorem better, so I wrote out a fairly explicit proof of the one-dimensional case.

    • I added a remark to inhabited set that one can regard writing AA\neq\emptyset to mean “AA is inhabited” as a reference to an inequality relation on sets other than denial.

    • I have begun an entry

      meant to contain detailed notes, similar in nature to those at Introduction to Stable homotopy theory (but just point-set topology now).

      There is a chunk of stuff already in the entry, but it’s just the beginning. I am announcing this here not because there is anything to read yet, but just in case you are watching the logs and are wondering what’s happening. In the course of editing this I am and will be creating plenty of auxiliary entries, such as basic line bundle on the 2-sphere, and others.

    • Just for procrastination purposes, yesterday I had started some minimum at asymptotic safety.

    • Carlos Simpson indicates that he takes issue with not having been cited by us and provides a list of references. Since the entry nonabelian cohomology was lacking a reference section until now, I took this as an opportunity to list Simpson's work and some other articles. But by far not exhaustive.

    • Since the question came up again on MO (here) I added to coimage a bit on the \infty-version.

    • At topological vector space, there's a spot where a uniform space is characterised by giving a base of entourages. Zoran thought that it would be a good way to make clear that ‘entourage’ is a technical term by making it into a link. So now there is a page entourage.

      Most of the details are still to be found at uniform space, however.

    • I am working on giving the entry on topology a section Introduction. This section is meant to provide persons with some background in, say, analysis, but otherwise with no idea of topology, briefly with some basic ideas. The basic definition, some pictures, the basic idea of how to use topological invariants in very simple examples, maybe culminating in an outline of the fundamental group and its relation to covering spaces. Not done yet.

    • Suppose somebody formally minded is looking for a good problem in the topic of contextual categories (C-systems). How about this:

      fix a given C-system, with your preferred set of extra type constructor data on it, and then ask the question: for any given small site, is the category of sheaves on that site with values in that C-system again canonically a C-system with the same collection of extra type constructors?

      I gather aspects of this play a role in most discussions of type theory model building, but is there any systematic discussion?

      I suppose the difficulty and interest in this question considerably varies with what the set of “extra type constructors” includes. A while back I had asked a similar question where “extra type constructors” was “modalities”. Maybe that was overambitious for the person who I am asking for, so I am trying to see if something along these lines but more tractable would be a good thing to aim at.

    • The entry closed subspace was a bit weird. I have touched it to try to improve a little. But if anyone has ten minutes to spare, it might still be good to bring this into more decent shape.

    • To make sense of this in my mind as a general concept, I have written semidefinite element. This gives a general context in which to define ‘positive definite’, ‘negative semidefinite’, ‘indefinite’ etc.

      (This seems the safest page title, as the least likely to have any conflicts. I've also put in a lot of redirects, but possibly some of these will have to go elsewhere; definite seems the most dangerous.)

    • Somehow I was under the impression that I had written out on the nnLab at several places how the traditional physics way to talk about instantons connects to the correct maths discussion. But now that I wanted to point a physicist to this, I realize that in each entry that touches on this, I just gave a quick remark pointing to Cech cohomology, clutching construction, one-point compactification and Chern-Simons 2-gerbes, but not actually giving an exposition.

      So I went ahead and wrote such an exposition finally:

      SU2-instantons from the correct maths to the traditional physics story

      Beware two things:

      1) this entry is meant to be included as a subsection into other entries (such as Yang-Mills instanton, BPTS instanton) therefore it is intentionally lacking toc, headlines and other introductory stuff

      2) I just wrote this in one go (trying to get back to somebody waiting for me), and now I am out of steam. This hasn’t been proof-read even once yet. So unless you feel energetic about joining in the editing, better wait until a little later when this has stabilized.

      Ideally this kind of account would eventually be beautified with some pictures and the like.

    • the entry category of sheaves had been a bit shy about giving away full information where it came to the recognition of epi/mono/isos. I have now expanded the proposition here.

      Maybe somebody feels inspired to add pointer to proof, or, better yet, add proof.

    • contrapositive now exists. It doesn't say much (unless you were unsure which versions of this rule are intuitionistically valid, in which case, you can take a look). But there was a link to it, so I made it.

    • Hi all,

      I've recently written my first all-on-my-own article, graded fusion category. I'll gladly welcome anyone looking over it and improving it (adding links, contents, improving formatting)
      I went on to work on a larger article, $G$-crossed braided fusion category, which is not quite finished yet. Here, help is appreciated as well. I'll go on adding more content over the next weeks, whenever I find time.

      I'm underwhelmed with the quality of the commutative diagram I could produce. I followed the example in monoidal category, which I thought must be state-of-the-art since it's a page about a really important concept. But I'm appalled with my result for the G-crossed braiding axiom in $G$-crossed braided fusion category. How can I improve it?
      I'll have a look at https://ncatlab.org/nlab/show/HowTo again later and see whether there is anything else that I can do.

      Manuel
    • started Fierz identity to collect some references. Am still searching for the good reference for the general case…