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: arity space

Bottom of Page

1 to 10 of 10

  1.  
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 24th 2019

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeJul 24th 2019

    Just kind of messing around here, but this seems like a natural common generalization of coherence spaces and finiteness spaces.

    v1, current

    • CommentRowNumber3.
    • CommentAuthorSam Staton
    • CommentTimeJul 25th 2019
    • (edited Jul 25th 2019)

    Nice. I think Girard-Loader totality spaces are κ={1}\kappa=\{1\}, right?

    Also, I thought these kinds of spaces will be always be *-autonomous because they’re built by double-gluing-along-hom-functors + orthogonality, right? (Section 5 of Glueing and orthogonality for models of linear logic, Hyland + Schalk, doi).

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJul 25th 2019

    Thanks for the pointer! Yes, it looks like totality spaces are unary spaces, except that totality spaces (in the reference I found) include the additional assumption that every element is contained in some unary subset and also some co-unary subset.

    Regarding double gluing and orthogonality, maybe, I’m not familiar with that and don’t have the time to understand it right now. Feel free to add to the entry!

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJul 25th 2019

    Added mention of totality spaces.

    diff, v2, current

    • CommentRowNumber6.
    • CommentAuthorSam Staton
    • CommentTimeJul 26th 2019

    A bit about generalizing to focuses in categories. It’s not much of a generalization and may be the best setting for this.

    diff, v3, current

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeJul 28th 2019

    Thanks! Maybe it would be better to have a separate page all about this kind of orthogonality, with interlinks?

    • CommentRowNumber8.
    • CommentAuthorSam Staton
    • CommentTimeJul 29th 2019

    link to double gluing

    diff, v4, current

    • CommentRowNumber9.
    • CommentAuthorSam Staton
    • CommentTimeJul 29th 2019

    moved text to double glueing page

    diff, v5, current

    • CommentRowNumber10.
    • CommentAuthormaxsnew
    • CommentTimeAug 18th 2022

    Sketch of the construction of arity spaces based on an orthogonality based on a comment. Maybe @Mike Shulman can see if it’s what he had in mind?

    diff, v6, current

1 to 10 of 10

  1.