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 comma 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 finite 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 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 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).
    • Specker sequences for non-computable numbers of interest in their own right.

      diff, v4, current

    • beginning to record some references – but nothing else here yet

      v1, current

    • starting something – not done yet but need to save

      v1, current

    • starting something – not done yet, but need to save

      v1, current

    • Starting something on Mike’s ideas here, as I wanted to refer to it.

      v1, current

    • I've started a page an elementary treatment of Hilbert spaces. The intention is to see how much of (simple) Hilbert space theory can be done without using the phrases "As a Hilbert space is a normed vector space ..." or "As a Hilbert space is a metric space ...".

      I haven't gotten very far yet, as can be seen! Also, it's not intended to be Deep Mathematics (there's a mild centipedal justification on the page) but just playing with some ideas and trying to see what a Hilbert space really is.

    • a bare minimum, so that the link exists

      v1, current

    • Have added more of the original (“historical”) References with brief comments and further pointers.

    • changed page name (previously “Dan Chirstensen”, which of course still redirects here)

      diff, v4, current

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

      v1, current

    • Can the nlab’s articles take in Javascript or Java applets? I was thinking of making a simple type theory parser for nlab’s pages with type theory (syntax much the same as type theory). For instance, I would make one to be embedded in the page on Lawvere’s diagonal argument. I have the theory sorted out already, so it’s just a matter of writing it up. I found an algorithm that simplifies triangle identities in worst case O( i=1 nm il)O(\sum_{i = 1}^n m_i l) where nn is the number of counits in a diagram, m im_i is the number of units in a diagram adjacent to a given counit. On average, m im_i and nn will be small in proportion to ll. (I’m interested to see if anyone can make a better triangle recognition algorithm for triangle identities in a strict 22-category - it seems there are tons of tricks one can do).

    • have added more items to the list, and re-arranged slightly here and there, for better systematics

      diff, v8, current

    • added pointer to:

      • Norman Steenrod, Homology With Local Coefficients, Annals of Mathematics, Second Series, Vol. 44, No. 4 (Oct., 1943), pp. 610-627 (jstor:1969099)

      • M. Bullejos, E. Faro, M. A. García-Muñoz, Homotopy colimits and cohomology with local coefficients, Cahiers de Topologie et Géométrie Différentielle Catégoriques, 44 no. 1 (2003), p. 63-80 (numdam:CTGDC_2003__44_1_63_0)

      diff, v4, current

    • It would seem that Vaughan Jones has died. I think that this was overnight on the 6th to 7th. Berkeley have ‘deceased’ on his page as an Emeritus professor. Does anyone else have more details? I have just checked on Wikipedia and they have changed their entry accordingly but with today’s date, which I think is wrong. I had the news via the MPPM network and someone at Vanderbilt university.

    • Created a page Morava K-theory . A lot to add. Will fill out later, with better reference list. Please edit!
    • am starting an entry here in order to record some facts. Not done yet

      v1, current

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

      v1, current

    • I worked on polishing

      Towards Higher Categories

      on John Baez's web. I

      • added hyperlinks to all the names appearing

      • turned the remaining "infininty"s to "oo"s

      I was almost done when the Lab broke down, though, it seems. Currently the server does not respond.

    • some minimum, for the moment just so as to record references

      v1, current

    • Has anyone thought about what geometric type theory would entail?

      I thought there might be something like this: we start with a dependent type theory. an infinitesimal extension object T(A) assigned to each A where A -> T(A) lifts against the smooth maps X -> Y, which play the role of fibrations. The infinitesimal interval plays the role of the path.

      An example would be sheaves over the big zariski site.
    • 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.

    • for completeness and ease of hyperlinking

      v1, current

    • Fibrations arise from the adjunction between context extension and dependent sum. They can also be defined by a certain lifting property, which coincides with identity type.

      I was wondering if there is a similar setup for cofibrations in a type theoretic paradigm. They are Eckmann Hilton dual, so I tried thinking about how to dualize the adjunctions that give rise to a fibration, but I didn’t get anywhere. However, a certain extension property seems related (I can’t quite tell what it should be), the one you get from dualizing the path space object construction.

      Does anyone know if there is a certain “co-context extension” and “codependent sum” which would give rise to cofibrations? Or really any setup.

    • added to gerbe

      • definition of GG-gerbes;

      • classification theorem by AUT(G)AUT(G)-cohomology;

      • the notion of banded GG-gerbes.

    • Changed paragraph regarding analytic versus algebraic proofs. I don’t think it is possible to give a purely algebraic proof of Weierstrass’s original theorem, whose conclusion includes the statement that the power series are convergent in some neighborhood of 00. How could you, when this is an analytic statement? I think my edit might be what the original author intended.

      David Speyer

      diff, v7, current

    • added to principal 2-bundle in a new Properties-section the classification results by Baez-Stevenson, Stevenson-Roberts (for the topological case) and Nikolaus-Waldorf (for the smooth case).

    • Started literature section with several references at forcing.

    • old page, repairing broken link

      Jon Awbrey

      v1, current

    • added more of the sections to the TOC, and more of their hyperlinked keywords

      diff, v3, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Following a post by Jim I have added a link to a lecture by Peter Hilton on the work at Bletchley Park with Alan Turing.