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 definitions 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 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).
    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 12th 2010

    I began writing the article club, with more to come.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeApr 12th 2010

    Thanks! I added some interspersed remarks about how clubs can be regarded as generalized operads, and asked a question.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 13th 2010

    Thanks for those additions, Mike. I responded to your question, and will probably export my answer to the text when I get the chance.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeApr 14th 2016

    I added a short section to club about the general notion of “club over a cartesian monad”, with a reference. (I don’t have at hand the correct references for the other versions; maybe some else can add them.)

    This is in preparation for hopefully generalizing it to cartesian monads in 2-categories other than CatCat, including Garner’s double clubs. Has anyone seen other such generalizations of the notion of club?

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeApr 20th 2017

    I did some work on club, mentioning the finite sets, many-objects, and over-Cat versions, and relating them all to polynomial monads. I am still rather puzzled by the mixed-variance case. I moved the parts of the query-box into the text that were not already there, except for a question and answer that I don’t fully understand. If mixed-variance clubs are the generalized operads for some cartesian monad, what is that monad? It can’t be polynomial. What are its algebras?

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeOct 26th 2017

    Re: #5, now I think maybe its algebras are strictly compact closed categories (i.e. symmetric strict monoidal categories equipped with a strictly involutive choice of duals) that are also enriched over pointed sets and such that all traces are the zero morphism. I can imagine it being cartesian.

    Is this version of the mixed-variance case, with the shape category enriched over pointed sets, in one of Kelly’s papers? I can’t find it right now.

    • CommentRowNumber7.
    • CommentAuthormikestay
    • CommentTimeJan 9th 2019
    What's the etymology of "club"? The social group or the weapon?
    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeJan 9th 2019

    Beats me. If I had to guess, I’d guess the social group, but it might be something entirely different.

  1. removing query box

    +–{: .query} Mike Shulman: Is this sort of club also a generalized operad for some cartesian monad on CatCat?

    Todd Trimble: I’m pretty sure that it’s a cartesian monad on CatCat, and actually I don’t know any real examples of Kelly’s clubs which aren’t. =–

    Anonymous

    diff, v24, current