Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science connection constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • created stub for smooth loci

      (should it be "smooth locus" instead?)

    • sty addition to generalized smooth algebra: remark on terminology added and section on "internal definition" added.

      planning to polish thinmgs later

    • created entry on Israel Gelfand with the material that John posted to the blog.

      turns out the "Timeline" entry was already requesting it

    • created microlinear space

      One thing I might be mixed up above:

      in the literature I have seen it seems to say that

      $ X^D x_X X^D \simeq X^{D(2)}$

      with

      $ D(2) = { (x_1,x_2) \in R \times R | x_i x_j = 0} $.

      But shouldn't it be

      $ D(2)' = { (x_1,x_2) \in R \times R | x_i^2 = 0} $.

      ?

    • quick addition of "formal infinitesimal spaces" and Weil algebras to infinitesimal space

      but am planning to polish this entry further later, it is a bit of a mess at the moment

    • A little more detail at natural isomorphism, including when one can speak of the functor satisfying certain conditions.

    • I worked on synthetic differential geometry:

      I rearranged slightly and then expanded the "Idea" section, trying to give a more comprehensive discussion and more links to related entries. Also added more (and briefly commented) references. Much more about references can probably be said, I have only a vague idea of the "prehistory" of the subject, before it became enshrined in the textbooks by Kock, Lavendhomme and Moerdijk-Reyes.

      Also, does anyone have an electronic copy of that famous 1967 lecture by Lawvere on "categorical dynamics"? It would be nice to have an entry on that, as it seems to be a most visionary and influential text. If I understand right it gave birth to topos theory, to synthetic differential geometry and all that just as a spin-off of a more ambitious program to formalize physics. If I am not mistaken, we are currently at a point where finally also that last bit is finding a full implmenetation as a research program.

    • created smooth topos on the axioms on toposes used in synthetic differential geometry.

    • By chance I came across an old CatTheory mailing list post by e. Dubuc, where he complains about how is work on SDG is not sufficiently recognized and asks people to speak of the "Dubuc topos".

      I added a remark about this to synthetic differential geometry in the section on "Well adapted models".

    • A few more sections at A Survey of Elliptic Cohomology - elliptic curves on

      • topol. invariants of the moduli stack of ell. curves

      • the compactified version

      • the definition of Gromov-Witten invariants

      • an example.

      As before, this is raw material which I am thinking lends itself to be turned into entries.

    • Added the Yoneda-embedding way to talk about group objects and hence supergroups.

    • A list of all recently edited entries can be seen at Recently Revised. But that list tends to contain lots of minor changes: it's not easy to spot the important ones. So, if you feel people's attention should be drawn to some changes you make, then please mention them here. This way the rest of us can spot them, so we can learn what you know — and maybe make further improvements!

      1. Go to the Latest Changes category in the Forum. If you are reading this on the forum, then you are there right now, or go to http://www.math.ntnu.no/~stacey/Vanilla/nForum/?CategoryID=5.
      2. Optionally, create an account (if you don't have one) and log in if necessary; this may be helpful but is not required.
      3. Hit ‘Start new discussion’ at the upper left.
      4. Choose a meaningful subject title, perhaps the name of the page you've edited or something like that.
      5. Write a brief message summarising your edit. Most of the formatting is the same as on the Lab if you choose the ‘Markdown+Itex’ radio button beneath the comment box.
      6. Please include a [[wikilink]] to the page or pages that you edited.
      7. If you didn't log in, then please also include your name.
      8. Check Preview Post (or skip it), and then Start your discussion!

      Questions? Ask them here!