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 categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration 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 lie-theory limit limits linear linear-algebra locale localization logic manifolds 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 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).
  1. Fixed a dead link to the Lack-Power paper

    Anonymous

    diff, v14, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 9th 2019

    I added the recent

    which considers this and related dualities in the enriched setting.

    diff, v15, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 9th 2019

    If we may think of ordinary Gabriel-Ulmer duality as operating between essentially algebraic theories and their categories of models, how should we think of the enriched version between 𝒱Lex\mathcal{V}-\mathbf{Lex}, the 2-category of finitely complete 𝒱\mathcal{V}-categories (𝒱\mathcal{V}-categories with finite weighted limits), finite limit preserving 𝒱\mathcal{V}-functors, and 𝒱\mathcal{V}-natural transformations, and 𝒱Lfp\mathcal{V}-\mathbf{Lfp}, the 2-category of locally finitely presentable 𝒱\mathcal{V}-categories, right adjoint 𝒱\mathcal{V}-functors that preserve filtered colimits, and 𝒱\mathcal{V}-natural transformations?

    Can I think of a finitely complete 𝒱\mathcal{V}-category as a kind of theory?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 9th 2019
    • (edited Jul 9th 2019)

    So in the case where 𝒱\mathcal{V} is the reals or the real interval, i.e., something along the lines of a Lawvere metric space, there appears to some connection to continuous logic

    • Simon Cho, Categorical semantics of metric spaces and continuous logic, (arXiv:1901.09077)

    with a “continuous subobject classifier”.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJul 9th 2019

    Re: #3: yes? (-:

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeJul 9th 2019

    Admittedly it may not be a very “syntactic” kind of theory…

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 4th 2019

    Gave an instance of the enriched version – meet semilattices and algebraic lattices.

    diff, v19, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)