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    • I have created brief stubs for cyclotomic field and anti-cyclotomic field. No real content there for the moment, just so as to make cross-links work and have a place to record references.

      I suppose what I am really looking for regarding discussion here in another thread is a concept of anti-cyclotomic spectrum.

    • a small entry for a finite group, really an unintended spin-off of compiling the character table of 2O (see discussion there)

      v1, current

    • I am compiling character tables of various groups. For ease of including into related entries (e.g. for isomorphic groups) I’ll give them their own little entries

      v1, current

    • have added to Topos in the section on limits of toposes the description of the pullback of toposes by pushout of their sites of definition.

    • I am compiling character tables of various groups. For ease of including into related entries (e.g. for isomorphic groups) I’ll give them their own little entries

      v1, current

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

      v1, current

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

      v1, current

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

      Matthew Weaver

      v1, current

    • I found myself writing permutation (since I had linked to it) and realised that I could even redirect symmetric group there (which has been linked to for some time).

      Pretty stubby now.

    • I am compiling character tables of various groups. For ease of including into related entries (e.g. for isomorphic groups) I’ll give them their own little entries

      v1, current

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

      v1, current

    • I am compiling character tables of various groups. For ease of including into related entries (e.g. for isomorphic groups) I’ll give them their own little entries

      v1, current

    • Added link to PDF file of Kobayashi’s book on Einstein-Hermitian vector bundles.

      N. Raghavendra

      diff, v4, current

    • added to localic geometric morphism the reference to Johnstone’s factorization-article and the statement that the internal locale corresponding to a localic geometric morphsm f:FE is f*(ΩF).

    • Felt sorry for the neglected β-rings, so started something.

      v1, current

    • Added Borger’s nice CT2018 talk.

      After recent chat about Burnside rings and β-rings, presumably the latter are related to some form of generalized symmetry.

      diff, v3, current

    • For completeness of cross-links, I have added this to the Examples-section:


      • In the Zariski topology on an algebraic variety Spec(R), the closed points correspond to the maximal ideals in R (this Prop.).

      • In particular the prime numbers correspond to the closed points in Spec(Z) (this Example).


      diff, v4, current

    • Stated Bertrand’s postulate and an equivalent formulation of it, and gave a proof of the latter (simple and in the literature, but recent and not very well known I believe) assuming that the Goldbach conjecture holds.

      v1, current

    • Clarified some confusing remarks about separation in different categories.

      diff, v9, current

    • added eom-pointer to the otherwise empty entry, fixed spurious whitespaces and missing letters in entry title

      diff, v2, current

    • am starting some minimum here, am really trying to see what is known regarding the following:

      Since, by the McKay correspondence, we may identify each vertex of a Dynkin quiver with the isomorphism class of an irreducible representation of the corresponding finite subgroup of SU(2) GADESU(2), a Bridgeland stability condition on representations of a Dynkin quiver directly restricts to a stability function on GADERep.

      But it feels that stability functions on the representation ring

      R(GADE)=K(GADERep)

      ought to have a really elementary expression in terms of basic objects of representation theory. Can one say anything here?

      In particular, the immediate reaction when asked to present a complex-valued function on reps is to just use their characters, maybe evaluated at some chosen conjugacy class, and probably normalized in some way.

      Is this known? Are there at least examples of stability functions on GADE-representation which have an elementary representation-theoretic expression, hopefully in terms of characters?

      This seems like it should almost be the first non-trivial example of stability conditions, but I have trouble finding any source that would make this explicit.

      v1, current

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

      v1, current

    • I added some closure properties of the class of proper morphisms of toposes and the proposition saying that a morphism of toposes is proper iff it satisfies the stable weak Beck-Chevalley condition to proper geometric morphism.

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

      v1, current

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

      Anonymous

      v1, current

    • am starting something. Just saving for the moment, not done yet

      v1, current

    • I added a Definition-section to AKSZ sigma-model with a bit of expanded discussion

    • Getting my contact info in for the communal initiality theorem project.

      Dave Ripley

      v1, current

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

      v1, current

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

      v1, current

    • Late last night I was reading in Science of Logic vol 1, “The objective logic”.

      I see that the idea of cohesion is pretty explicit there, not in the first section of the first book (Determinateness, which has the discussion of “being and becoming” that Lawvere is alluding to in the Como preface) but in the second section of the first book, “The magnitude”.

      There the discussion is all about how the continuous is made up from discrete points with “repulsion” to prevent them from collapsing to a single and with “attraction” that keeps them together nevertheless.

      This “attraction” is clearly just the same idea as “cohesion”. One can play this a bit further and match Hegel’s Raunen to formal expressions involving the flat modality and the shape modality pretty well. I made some quick notes in the above entry.

      On the other hand, that section 1 about being and becoming seems to be more about the underlying type system itself. Notably about the empty type and the unit type, I think

    • The definition of braided monoidal category was wrong or at least nonstandard, because it left out one of the hexagon axioms and included a 'compatibility with the unit object' law which follows from the usual definition.

      I changed it to the usual definition.

      If the nonstandard definition is equivalent to the usual one, I'd love to know why! But I don't see how you get two hexagons from one, even given compatibility with the unit object.

      (Of course for a symmetric monoidal category we just need one hexagon.)

      I also beefed up the definition at symmetric monoidal category so the poor reader doesn't need to run back to braided monoidal, then monoidal.
    • Added some remarks, mostly about extensivity and exactness, to quasitopos.

    • Now there is Sylow p-subgroup.


      Is there a compilation, somewhere, of the results “the (obvious) automorphisms of a small 𝔄 A are transitive on A’s maximal 𝔅s?” The only other example ready in my head is that the maximal tori in a compact Lie group are conjugate, but I know I’ve seen more.

    • Fixed a typo, but also I noted the last but one link is dead. Does any one know if this has moved somewhere?

      (Edit: I found it. There is a link from his home page. I have updated the link.)

      diff, v7, current

    • I am giving this generalized homology theory its own little entry, so that it becomes possible to refer to it more specifically, beyond broadly pointing to just “stable homotopy groups”.

      (Curious that things are set up such that the most fundamental of homology theories is almost un-nameable, since its canonical name clashes with the name of the whole subject. Curious circularity there.

      The other day I was visiting the Grand Mosque. It’s qibla wall has a huge mosaique displaying the 99 names of God in 99 flowers, plus one flower with no name it in, to represent the un-nameable (one can see it well here, only that the sheer size of it is not brought across by photographs). )

      v1, current

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

      v1, current