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    • I have started on a revision of algebraic K-theory. The old version launched straight into a particular nPOV, which really just summarised the Blumberg et al paper, and did not mention any of the other ideas in the area. At present I have just put in some historical stuff, but given the importance of the subject e.g. in modern C*-algebra the page needs a lot more work.

    • am changing page name from “…F-theory…” to “…M/F-theory” since I will now add discussion and references in that more general case

      diff, v12, current

    • definition of ll-lagrangian subspaces from

      • Manuel de León, David Martín de Diego, Aitor Santamaría-Merino. Tulczyjew’s triples and lagrangian submanifolds in classical field theories (2003). (arXiv:math-ph/0302026).

      should also include Definition 3.18 from that paper (ll-lagrangian submanifolds) somewhere but there are at least two different relevant entries (multisymplectic geometry, n-plectic geometry).

      diff, v2, current

    • Added doi link and pages for Spanier’s original article

      diff, v6, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Create a stub. I will expand the list shortly.

      v1, current

    • This is a page about the metamath proof assistant. I’m not very expert but it’s a start.

      Roger Witte

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Added references for the path integral approach.

      diff, v4, current

    • added a few more words to this entry, but it remains a stub

      diff, v2, current

    • The link for ’equivalent’ at the top redirected to natural isomorphism which (as I understand it) is the correct 1-categorical version of an equivalence of functors, but this initially lead me to believe that a functor was monadic iff it was naturally isomorphic to a forgetful functor from the Eilenberg-Moore category of a monad on its codomain, which would mean that the domain of the functor was literally the Eilenberg-Moore category of some adjunction since natural isomorphism is only defined for parallel functors.

      diff, v19, current

    • I have renamed the entry formerly called (and still redirecting) “connection on a principal infinity-bundle” into connection on a smooth principal infinity-bundle.

      I will now start with bringing that entry into shape.

      In the same vein I have renamed the entry formerly titled (and still redirecting) “infinity-Chern-Weil theory” into Chern-Weil theory in Smooth∞Grpd.

      This way things are set up well for when the legions of students arrive who will do all the analogous discussion in other cohesive (∞,1)(\infty,1)-toposes such as Algebraic∞GrpdAlgebraic \infty Grpd, ComplexAnalytic∞GrpdComplexAnalytic \infty Grpd as well as the derived version of all of these. ;-)

    • brief category:people-entry for hyperlinking references

      v1, current

    • added references and various quick remarks, such as that the subspace of Cayley 4-planes

      CAY⊂Gr(4,8) CAY \subset Gr(4,8)

      has this coset space structure:

      CAY≃Spin(7)/(Spin(4).Spin(3)) CAY \;\simeq\; Spin(7)/\big( Spin(4).Spin(3)\big)

      I am guessing we also have

      ⋯≃Spin(8)/(Spin(5).Spin(3)) \cdots \simeq Spin(8)/\big( Spin(5).Spin(3)\big)

      (??)

      diff, v3, current

    • starting to collect references on string/M-theory compactifications on K3-compactifications (here). Am also touching related entries such as Moonshine etc.

      diff, v14, current

    • Added a reference to

      • Christian Maurer, Universes in Topoi , pp.285-296 in Lawvere, Maurer, Wraith (eds.), Model Theory and Topoi , LNM 445 Springer Heidelberg 1975.

      diff, v19, current

    • Added remark on geometric realizations of pairs of adjoint functors

      Roman T

      diff, v17, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • This is a bare list of references, to be !include-ed into relevant entries, such as at swampland and 24 branes transverse to K3, for ease of cross-linking and updating.

      I am taking the liberty of including a pointer to our upcoming M/F-Theory as Mf-Theory which has some details on a precise version of the conjecture and a proof (from Hypothesis H).

      v1, current

    • Someone deleted the contents of the entry simplicial localization on th 4 April, then another reinstated it on the 5th. Curious!

    • created a page with empty contents.

      Kensuke Arakawa

      v1, current

    • added to complete Segal space a discussion of what an ordinary category looks like when regarded as a complete Segal space.

      (This is meant to be pedagogical, therefore the recollection of all the basics at the beginning.)

    • Anel and Catren in their introduction to New Spaces in Physics claim that Lagrangian submanifolds are category-theoretic “points” of a symplectic manifold, morphisms from the trivial symplectic manifold in Weinstein’s symplectic category.

      Is this accurate?

      Anonymous

      diff, v19, current

    • The entry on topological group could stand more work, but I added some stuff on the uniform structure, in particular the proposition that for group homomorphisms f:G→Hf: G \to H, continuity at a single point guarantees uniform continuity over all of GG. The proof is follow-your-nose, of course.

      What we really need is an entry Haar measure. I’ll get started on that soon.

    • At coverage, I just made the following change: Where the sheaf condition previously read

      X(U)→∏ i∈IX(U i)⇉∏ i,j∈IX(U i× UU j), X(U) \to \prod_{i\in I} X(U_i) \rightrightarrows \prod_{i,j\in I} X(U_i\times_U U_j),

      it now uses the variable names “jj” and “kk” instead of “ii” and “jj”:

      X(U)→∏ i∈IX(U i)⇉∏ j,k∈IX(U j× UU k). X(U) \to \prod_{i\in I} X(U_i) \rightrightarrows \prod_{j,k\in I} X(U_j\times_U U_k).

      I’m announcing this almost trivial change because I’d like to invite objections, in which case I’d rollback that change and also would not go on to copy this change to related entries such as sheaf. There are two tiny reasons why I prefer the new variable names:

      • It’s more symmetric. The previous notation unjustly favored “ii”.
      • It’s slightly easier to infer the definition of the two maps. (I had a student who was briefly confused by the original notation.)

    • a category:activity-page for hyperlinking references to a new conference series which we are organizing

      v1, current

    • In discrete fibration I added a new section on the Street’s definition of a discrete fibration from AA to BB, that is the version for spans of internal categories. I do not really understand this added definition, so if somebody has comments or further clarifications…

    • Todd,

      when you see this here and have a minute, would you mind having a look at monoidal category to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?

      Thanks!

    • The filtered limit is typo of filtered colimit

      peter

      diff, v4, current

    • a stub entry, for the moment just to make the link work

      v1, current

    • throw out scratch notes from a bajillion years ago

      Blake C. Stacey

      diff, v14, current

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