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    • 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

    • created Einstein’s equation, only to record a writeup by Gonzalo Reyes which I just came across by chance, who gives a discussion in terms of synthetic differential geometry.

    • finally created the category:reference-entry for Lurie’s chromatic lecture. See Chromatic Homotopy Theory

      (And as a special service to the community… with lecture titles. ;-)

      • Lecture 1 Introduction (pdf)

      • Lecture 2 Lazard’s theorem (pdf)

      • Lecture 3 Lazard’s theorem (continued) (pdf)

      • Lecture 4 Complex-oriented cohomology theories (pdf)

      • Lecture 5 Complex bordism (pdf)

      • Lecture 6 MU and complex orientations (pdf)

      • Lecture 7 The homology of MU (pdf)

      • Lecture 8 The Adams spectral sequence (pdf)

      • Lecture 9 The Adams spectral sequence for MU (pdf)

      • Lecture 10 The proof of Quillen’s theorem (pdf)

      • Lecture 11 Formal groups (pdf)

      • Lecture 12 Heights and formal groups (pdf)

      • Lecture 13 The stratification of ℳ FG\mathcal{M}_{FG} (pdf)

      • Lecture 14 Classification of formal groups (pdf)

      • Lecture 15 Flat modules over ℳ FG\mathcal{M}_{FG} (pdf)

      • Lecture 16 The Landweber exact functor theorem (pdf)

      • Lecture 17 Phanton maps (pdf)

      • Lecture 18 Even periodic cohomology theories (pdf)

      • Lecture 19 Morava stabilizer groups (pdf)

      • Lecture 20 Bousfield localization (pdf)

      • Lecture 21 Lubin-Tate theory (pdf)

      • Lecture 22 Morava E-theory and Morava K-theory (pdf)

      • Lecture 23 The Bousfield Classes of E(n)E(n) and K(n)K(n) (pdf)

      • Lecture 24 Uniqueness of Morava K-theory (pdf)

      • Lecture 25 The Nilpotence lemma (pdf)

      • Lecture 26 Thick subcategories (pdf)

      • Lecture 27 The periodicity theorem (pdf)

      • Lecture 28 Telescopic localization (pdf)

      • Lecture 29 Telescopic vs E nE_n-localization (pdf)

      • Lecture 30 Localizations and the Adams-Novikov spectral sequence (pdf)

      • Lecture 31 The smash product theorem (pdf)

      • Lecture 32 The chromatic convergence theorem (pdf)

      • Lecture 33 Complex bordism and E(n)E(n)-localization (pdf)

      • Lecture 34 Monochromatic layers (pdf)

      • Lecture 35 The image of JJ (pdf)

    • I recently created entry Bol loop. Now I made some corrections and treated the notion of a core of a right Bol loop (the term coming allegedly from Russian term сердцевина).

    • started stubs E-∞ geometry, E-∞ scheme.

      To be filled with more content, for the moment I just need to be able to use the links.

    • created A Survey of Elliptic Cohomology - elliptic curves with seminar notes on an exposition on elliptic curves.

      Am hoping that some kind soul will eventually further go through these seminar notes and copy bits of material to separete entries, where it belongs. Eventually.

    • I have created a stub for n-truncation modality and cross-linked with double negation modality.

      I gather that double negation = (-1)-truncation in a “predicative context”, but maybe I don’t fully understand yet what predicativity has to do with it.

    • felt like the nLab should have an entry fraction

    • Popped my head round the door and made a couple of changes to Banach algebra

      The first change was to attempt a more lax position on what should constitute a Banach coalgebra: only looking at comonoids in the monoidal category of Banach spaces (geometric or topogical) with projective tensor product would rule out several important examples that have arisen in e.g. abstract harmonic analysis. The existence of different monoidal structures in the category of Banach spaces is a pain, but without it one would miss out on a rich world of examples.

      The second was to add, to the list of examples, the celebrated-in-my-world-and-possibly-no-others Arens products on the double dual of a Banach algebra. I’ve made a stab at linking them to the related concepts of tensorial strength and strong monad but would welcome feedback or improvements.

    • isotope (physics) and isotope (algebra) with redirect for isotopy (algebra). I have read and thought much about isotopies in last couple of weeks, but no time at this point to write much about it into nnLab.

    • … need not be 11, but it shouldn't be larger; remarks about this are now at Banach algebra (and also at JB-algebra).

    • There is a deliberately ambiguous stub at finite-dimensional space.

      We might collect there all of the nice things about finite-dimensional spaces (for various notions of ’space’).

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