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    • I wrote analytic function, mostly just a definition. I found a reference that treated the infinite-dimensional case in pretty fair generality (slightly more than I actually did) without making the definition any more complicated (well, except one place where one must insert the word ‘continuous’), so I did that.

    • I added a reference to C-star-system. I propose that we change the name of the page to the C-star dynamical system; this is the standard full term, jargon which is skipping dynamical is confusing for an outsider and not explicative. I can imagine many other things which deserve that name.

    • I have cross-linked de Morgan duality with Wirthmüller context for the statement that in linear logic

      ∏ f∘𝔻≃𝔻∘∑ f. \prod_f \circ \mathbb{D} \simeq \mathbb{D} \circ \sum_f \,.

      Also I have tried to make more of the links in the tables at de Morgan duality point to something.

    • The convention, when describing ring extensions, everywhere I’ve seen a convention, is that

      • for SS a set of primes, “localize at SS” means “invert what is not divisible by SS”; so for pp prime, localizing “at pp” means considering only pp-torsion.
      • adjoining inverses [S −1][S^{-1}] is pronounced “localized away from SS”. Inverting a prime pp is localizing away from pp, which means ignoring pp-torsion.

      I have adjusted four instances of former “at” on three pages that would be, algebraicwise, “away from” (and so they now appear).

      Evidently, this conflicts with more-categorial uses of “localized”; “inverting weak equivalences” is called localization, by obvious analogy, and is written as “localizing at weak equivalences”. This is confusing! It’s also weird: since a ring is a one-object AbAb-enriched category with morphisms “multiply-by”, the localization-of-the-category RR “at pp” (or its AbAb-enriched version, if saying that is necessary) really means the localization-of-the-ring RR “away from pp”.

      You all can sort out that contravariance as/if you like, but don’t break the old algebra papers!

    • Added to field examples of internal fields: the canonical ring objects of the petit resp. gros Zariski toposes of a scheme.

    • Started an entry on closed morphisms, containing examples and characterizations using the internal language. Then I noticed that an entry on closed map already exists, but at the moment the nLab is too slow for proper browsing and editing. Will finish later and maybe merge the entries.

    • I repaired the definition of “unramified morphism” of schemes.

    • I noticed that the two links : André Joyal, The theory of quasicategories and its applications lectures at Simplicial Methods in Higher Categories, (pdf), near the bottom of the entry join of quasi-categories are dead. Does anyone have a more recent link? or if not an alternative reference?

    • I have added the following reference to Berkovich space. Judging from the abstract this sounds like I nice unifying perspective. But I haven’t studied it yet

      • Oren Ben-Bassat, Kobi Kremnizer, Non-Archimedean analytic geometry as relative algebraic geometry (arXiv:1312.0338)

      We show that Berkovich analytic geometry can be viewed as algebraic geometry in the sense of Toën-Vaquié-Vezzosi over various categories. The objects in these categories are vector spaces over complete valued fields which are equipped with additional structure. The categories themselves will be quasi-abelian and this is needed to define certain topologies on the categories of affine schemes. We give new definitions of categories of Berkovich analytic spaces and in this way we also define (higher) analytic stacks. We characterize in a categorical way the G-topology or the topology of admissible subsets used in analytic geometry. We demonstrate that the category of Berkovich analytic spaces embeds fully faithfully into the categories which we introduce. We also include a treatment of quasi-coherent sheaf theory in analytic geometry proving Tate’s acyclicity theorem for quasi-coherent sheaves. Along the way, we use heavily the homological algebra in quasi-abelian categories developed by Schneiders.

    • I wanted to collect some of the stuff recently added to a bunch of chromatic entries in a way that forms an at least semi-coherent story, so I made an entry

      This is built mostly from copy-and-pasting stuff that I had added to dedicated entries, equipped with a bit of glue to make it stick together and form a story.

      (Special thanks to Marc Hoyois for general discussion and in particular for working on the text on the Lurie spectral sequence.)

      I want to further fine-tune this. But not tonight.

    • as you may have seen in the logs, I am working on an entry Higher toposes of laws of motion, something like extended talk notes.

      I am running a bit out of time, and so the entry is unpolished and turns into just a list of keywords towards the end, for the moment. But in case anyone is wondering about the logs, here is the announcement.

      Don’t look at this yet if you feel like just reading. Of course if you feel like joining in with the editing a bit, that’s welcome, as usual.

    • I split off an entry dg-geometry from the entry on Hochschild geometry, since it really deserves a stand-alone discussion.

      Eventually somebody should add the references by Kapranov et al on dg-schemes etc. And much more.

    • stub for infinitesimal extension (and cross-linked a bit)

      Zoran: sorry, I know I should cite that article of yours/your colleagues, could you please add it? Thanks.

    • as last week, I have created an entry that collects some of the recent edits scattered over the nLab supposedly in one coherent story, it’s

      basics of étale cohomology

      Should be expanded a bit more. But not tonight.

    • At the entry classifying morphism, there is a query (not displayed as one):

      Where can I find a construction of the classifying morphism to a classifying space for a G-bundle with connection - using the connections as a 1-form?

      Given the subject matter and the name ‘jim’ plus the location of 96.245.205.76 (Pennsylvania …)????

    • at Artin-Schreier sequence I spelled out the existence proof. This derserves/demands to be further polished and streamlined, but i’ll leave it at that for the moment.

    • in my search for a good way of introducing basics of étale cohomology I switched from Milne to Tamme, and started some hyperlinked index for the latter’s Introduction to Étale Cohomology. As before, in the course of this I created some brief entries for keywords there, if they didn’t exist yet.

      Hope to expand this now…

    • Fixed a couple incorrect statements at hypercomplete (infinity,1)-topos:

      • Remark 1 claimed that having enough points in the 1-topos sense implies having enough points in the ∞-sense. I replaced it with a counterexample from HTT.
      • In Proposition 1 I replaced “finite homotopy dimension” by “locally of homotopy dimension ≤n\leq n”.

    • I have started a hyperlinked index for Milne’s Lectures on Étale Cohomology

      (Up to and including section 27, where the proof of the Weil conjectures starts. )

      In the course I have created a bunch of brief entries, if the corresponding keyword didn’t yet have one. Also cross-linked vigorously.

    • added to the list of equivalent conditions in the definition at étale morphism of schemes the pair “smooth+unramified”. Added a remark after the definition on how to read these pairs of conditions.

    • we had an entry spectrum (geometry) which wasn’t linked to from almost anywhere, in particular not from spectrum - disambiguation.

      I have now added a bunch of cross-links, between these two entries and between the entries that they link to. It’s better now than it was before, but could still do with further improvement.

    • I have fixed some dead links relating to Loday which were occurring n several pages.

    • made a note of a simple observation:

      for XX an atom in a cohesive ∞\infty-topos H\mathbf{H} over ∞Grpd\infty Grpd, then also the slice H /X\mathbf{H}_{/X} is cohesive … except possibly for the property that shape preserves binary products (but it does preserve the terminal object):

    • I noted an entry on generalized Eilenberg-MacLane spaces, but note that there is another use of this term in the literature, namely the representing fibrations for cohomology with local coefficients. These are the fibrations used by Gitler and then by Alan Robinson, Hans Baues and others more recently. What would be the preferred name for these latter things. (I personally find the idea of giving a name to products of Eilenberg- Mac Lane spaces other that ‘products of Eilenberg - Mac Lane spaces’ a bit strange, but I know that there is some strange terminology around!)

    • I noticed by accident that we have an entry coinvariant. Then I noticed that we also have an entry homotopy coinvariant functor.

      I have now added cross-links between these entries and with invariant and orbit, so that they no longer remain hidden.

      I also edited the first case of group representation coinvariants at coinvariant a little.

    • I noticed that some old entries were requesting a keyword link for brave new algebra, so I created it and filled in a default-paragraph. Please feel invited to expand.

      In that context I have a question: the dual generlized Steenrod algebras have been called “brave new Hopf algebroids” in articles including

      But the Hopf algebroids considered in these articles are ordinary Hopf algebroids, they are given not by Hopf ∞\infty-algebras (E,E∧E)(E, E \wedge E) but by their homotopy groups (E •,E •(E))(E_\bullet, E_\bullet(E)), unless I am missing something.

      So at least without further discussion, calling (E •,E •(E))(E_\bullet, E_\bullet(E)) “brave new” is a bit of a stretch. The brave new thing would be (E,E∧E)(E, E \wedge E) (if indeed it is a “Hopf ∞\infty-algebroid”).

      Can anyone say more about this? I can’t seem to find any source talking about this. The canonical guess of googling for “derived Hopf algebroid” doesn’t show relevant results.

    • some basics at Lubin-Tate theory

      (wanted to do more, but the nLab is giving me a really hard (down-)time )

    • created a table-for-inclusion image of J – table listing pertinent information in low degree, and included it in some relevant entries

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