Not signed in (Sign In)

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 book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry 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 homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics 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 sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft 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).

nLab > Latest Changes

Show all

11701 to 11760 of 14381

  1. <
  2. 1
  3. ...
  4. 192
  5. 193
  6. 194
  7. 195
  8. 196
  9. 197
  10. 198
  11. 199
  12. ...
  13. 240
  14. >

    • added to the people-entry Maxim Kontsevich in the list of the four topics for which he received the Fields medal brief hyperlinked commented on what these keywords refer to.

    • created etale geometric morphism

      (david R.: can we count this as a belated reply to your recent question, which I can’t find anymore?)

    • I am writing some notes for a talk that I will give tomorrow:

      I thought this might serve also as an exposition for a certain topic cluster of nnLab entries, so I ended up typing it right into the nnLab.

      Notice that this is presently a super-rough version. At the moment this is mostly just personal jotted notes for myself. There will be an abundance of typos at the moment and at several points there are still certain jumps that in a more polished entry would be expanded on with more text.

      So don’t look at this just yet if you have energy only for passive reading.

    • This is failing to load (on Firefox). I have tried several times and the error message changes each time! The latest was:

      XML Parsing Error: no element found Location: http://ncatlab.org/nlab/show/category+of+fibrant+objects Line Number 1350, Column 39: (N \mathbf{B}(-,G))_1 : U \mapsto C( ————————————–^

      I have also tried it in Safari and the page does not load beyond a certain point.

    • I think there was some terminological confusion, where the nLab defined Segal’s category Γ\Gamma to be a skeleton of finite pointed sets; I think it should be the category opposite to that. I’ve made edits at this article and at Gamma-space.

    • added a paragraph about passing from first-order logic to modal type theory to the entry on analytic philosophy.

    • I’ve made comments at Fivebrane, fivebrane 6-group, Fivebrane structure and differential fivebrane structure regarding the fact String(n)String(n) is not 6-connected for n≤6n \leq 6 (though trivially so for n=2n=2).

      There will be a bunch of interesting invariants for manifolds of dimensions 3-6. This includes, for instance, on 6-dimensional spin manifolds a non-torsion class corresponding to the obstruction to lifting the tangent bundle to the 6-connected group covering String(6)String(6) (here π 5(String(6))=ℤ\pi_5(String(6)) = \mathbb{Z}). This is the only non-torsion example, but should be given by a U(1)U(1)-4-gerbe, I think, which will have a 6-form curvature. Since H 6H^6 won’t be vanishing for oriented manifolds, one has some checking to do. For instance, the frame bundle of S 6S^6 lifted to a String(6)String(6)-bundle (I plan to write a paper on this 2-bundle) will not lift to a Fivebrane(6)Fivebrane(6)-bundle, because it won’t even lift to a String(6)˜\widetilde{String(6)}-bundle (i.e. the 6-connected cover of String(6)String(6)), since the transition function S 5→BString(6)S^5 \to BString(6) is the generator. Thus the 6-form curvature of this 4-gerbe should be the volume form on the 6-sphere.

      Another point that occurs to me is that there are two copies of ℤ\mathbb{Z} to kill off in String(8)String(8) to get Fivebrane(8)Fivebrane(8), so one gets a U(1)×U(1)U(1)\times U(1) higher gerbe. I suspect this larger π 7\pi_7 is why there are so many more exotic spheres in dimension 15 than in neighbouring dimensions (16256 vs 2 in d=14 and 16); it’s certainly the case for exotic spheres in dimension 7 that π 3(SO(4))=ℤ×ℤ\pi_3(SO(4)) = \mathbb{Z}\times \mathbb{Z} helps.

    • Here we are going to explain the application of Topology.

    • have highlighted a bit more the fact here that the atoms in a subtopos lattice are the 2-valued Boolean ones. Thanks to Thomas Holder for alerting me.

      And have added this as an example/proposition to atom and to Boolean topos, too.

    • I threw in some references to the early topos approach to set theory in ETCS. On this occasion I couldn’ t resist the temptation to rearrange somewhat the lay-out of the entry: actually I thought it better not to throw HOTT immediately at the reader and gave Palmgren’s ideas a proper subsection. I’ve also deflated a bit the foundational claims of ETCS sticking more to what appears to me to be Lawvere’s original intentions.

    • This comment is invalid XML; displaying source. <p>I created <a href="https://ncatlab.org/nlab/show/synthetic+differential+geometry+applied+to+algebraic+geometry">synthetic differential geometry applied to algebraic geometry</a> which is supposed to host a question that I am going to post on <a href="http://go2.wordpress.com/?id=725X1342&site=sbseminar.wordpress.com&url=http%3A%2F%2Fmathoverflow.net%2F">math Overflow</a> following the discussion we have of that <a href="http://sbseminar.wordpress.com/2009/10/14/math-overflow/#comment-6875">here at SBS</a>.</p> <p>In that context I also wrote a section at <a href="https://ncatlab.org/nlab/show/algebraic+geometry">algebraic geometry</a> intended to describe the general-nonsense perspective. But that didn't quite find the agreement with Zoran and while we are having some discussion about this in private, he has restructured that entry now.</p>
    • I've asked John Barrett recently and he agrees that the Yetter model and the Crane-Yetter model are two different things. I've written about that in a new article: http://ncatlab.org/nlab/show/Crane-Yetter+model

    • brief entry on Turaev-Viro model, an entry long overdue. But for the moment it just records some references.

      Bruce Bartlett has a comment on what is currently the last of these references and he will post it below in a moment…

    • am creating

      2d TQFT – table

      listing the statements of the classification results, for the various cases. As far as I am aware of them.

    • gave 2d TQFT a slightly more informative Idea-section, highlighting the difference between the classical strict case classified by Frobenius algebras and the local/extended non-compact case classified by Calabi-Yau objects.

      Added a reference by Abrams as a candidate for a first rigourous proof of the classification result via Frobenius algebras, and added citations for the local case (copied over from TCFT).

    • Created a stub at Milnor K-theory, which is now just an MO answer of Cisinski. To be expanded at some later point when I study this in more detail.

    • I corrected the page overconvergent global analytic geometry about the global unitary group: it is not a group (in the archimedean setting) but a strict analytic $\infty$-groupoid.

      One may thus define $BU(n)$ but the naive space $U(n)$ is not a group.

      In any case, one can still work with $BU(n)$ as if it were a classifying stack, i guess...

      It would be interesting to see if some of the ideas of geometric Langlands still make sense in this setting. Any comments on this?

      And on the possibility of doing higher Chern-Simons using this strange $BU(n)$, Urs?
    • I added this topic because it seems to be the right setting for motivic homotopy theory of overconvergent global analytic spaces (if one wants to have a relation with global Hodge theory in the sense of another entry of nlab).

      Cheers,

      Fred

    • I added two new important references on global analytic geometry, also due to Poineau. He shows there that the sheaf of analytic functions is coherent. This is an interesting fundamental result.

    • Couldn’t find an existing “latest changes” thread for the quasifibration page (http://ncatlab.org/nlab/show/quasifibration), but just wanted to remark that I put another reference in there, to a nice expository paper by Peter May.

      -Jon

    • I wrote a little piece at general covariance on how to formalize the notion in homotopy type theory. Just for completeness, I also ended up writing a little blurb at the beginning about the genera idea of general covariance.

    • I have added pointer to Mike’s discussion of spectral sequences here at “homotopy spectral sequence” and in related entries.

      But now looking at this I am unsure what the claim is: has this been formalized in HoTT?

      (Clearly a question for Mike! :-)

    • expanded the entry cofinal functor: formal definition, list of equivalent characterizations and textbook reference.

    • Hi guys and girls,

      I have set up a new subject on the nlab, related to the previously opened subject of global Hodge theory:

      http://ncatlab.org/nlab/show/Arithmetic+cryptography

      Contributions are welcome (in particular to fill-in the blanc subjects on this page, if you like).

      Fred
    • Hi guys,

      I plan to improve drastically the content of the nlab on Hodge theory, p-adic, classical and global.

      With this perspective in mind, i have made some new topics, and improved the section on global analytic geometry, by adding in particular a new reference of mine that contains a notion of strict global analytic spaces and some perspectives for its use to study various problems of arithmetic geometry.

      The new topics, that should be the place to discuss these subjects if you are interested, are: generalized Lambda-structures and global Hodge theory. I also plan to make a page on special values of L-functions, and another on the spectral interpretation of zeroes and poles of L-functions.

      I don't connect often to the nforum, so i may not discuss a lot about the present message, but the nlab pages will be updated. Contact me by email at frederic.paugam@imj-prg.fr if you would like to discuss these things.

      All the best,

      Frédéric

    • How would you define the usual jargon “fragment” in logic?

      There ought to be a simple formal definition, I suppose, such as “Given a language L and a theory T in that language, then a fragment of T is… “

    • Discussion with Mike reminded me that we were lacking an entry reflective subuniverse.

      I started a template and cross-linked, but now I am out of battery and time before filling in any content. Will do that tomorrow.

    • This is to flag up two entries that so-far just have titles. They are IulianUdrea and perfectly normal space. These may need watching. The second may be ok, and be a page somone has just started and intends to continue, but the name on the second also occurs as a name on a Mo page with no questions and no answers and may be someone seeing how many wikis etc they can put stuff on! Sorry for being a nasty suspicious b*****, but it looks a bit strange to me.

      (N.B., the two entries do not seem to be related.)

    • at diffeomorphism I started listing theorems and references on statements about when the existence of a homeomorphism implies the existence of a diffeomorphism.

      I dug out ancient references for the statement that in d≠4d \neq 4 everything homeomorphic to an open dd-ball is also diffeomorphic to it. What would be a more modern, more canonical, more textbook-like reference for this?

      And I’d also like to cite a reference for what is maybe obvious, that if that something in d=4d = 4 is an open subset of ℝ 4\mathbb{R}^4 equipped with the induced smooth structure of the standard smooth structure, then the statement is also true in that dimension.

      In fact, I am looking for nice/explicit/useful diffeomorphisms from the open nn-ball onto the open nn-simplex. I can of course fiddle around and cook up something, but I haven’t found anything that would count as nice. But probably some engineer out there working with finite elements or something does have a convenient choice.

    • there is this new master thesis:

      • Cesare Gallozzi, Constructive Set Theory from a Weak Tarski Universe, MSc thesis (2014)

      which discusses aspects of weak Tarskian homotopy type universes following the indications that Mike Shulman has been making, for instance at universe (homotopytypetheory). I just got permission to share this and I have now included pointers to the thesis to that entry, to type of types, etc.

    • At some point I had made up the extra axiom/terminology saying that an object 𝔸 1\mathbb{A}^1 in a cohesive ∞\infty-topos “exhibits the cohesion” if the shape modality is equivalent to 𝔸 1\mathbb{A}^1-localization. Now I was talking about that assumption with Mike and noticed that this didn’t have a reflection on the nnLab yet.

      So now I have added, for the record, the definition here at “cohesive oo-topos” and cross-linked with the existing discussion at “continuum”.

    • added recent AlgTop mailing list contribution on fibrant replacement of cubical sets to cubical set

11701 to 11760 of 14381

  1. <
  2. 1
  3. ...
  4. 192
  5. 193
  6. 194
  7. 195
  8. 196
  9. 197
  10. 198
  11. 199
  12. ...
  13. 240
  14. >
Top of Page