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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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).
    • CommentRowNumber1.
    • CommentAuthorThomas Holder
    • CommentTimeOct 11th 2014

    I’ve written a stub on Cole’s theory of spectrum which for the time being consists largely of references and links. Further curation or correction would be appreciated!

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 11th 2014
    • (edited Oct 11th 2014)

    Thanks! I suppose this is the abstract concept of spectrum also considered in Structured Spaces.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 11th 2014

    I changed some wording in the definition section ever so slightly.

    • CommentRowNumber4.
    • CommentAuthorThomas Holder
    • CommentTimeOct 11th 2014

    Thanks! I’ve added some further material from the account in Johnstone 1977. There Johnstone attributes the observation of the right adjointness property of spec to Hakim. Cole’s construction yields some standard examples. I don’t know enough about Hakim’s or Lurie’s work to see how Cole’s stuff is precisely related to theirs. I’ve added a link to Structured Spaces though.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 11th 2014
    • (edited Oct 11th 2014)

    Thanks.

    We have an old stubby entry with the sweet name locally algebra-ed topos which is effectively about this concept of “TT-modelled topos”, up so some evident variants. For the time being I have made T-modelled topos redirect to that. Eventually one might split off a separate entry, or rename that existing entry, and in any case expand further (maybe by copying the relevant section from Cole’s theory of spectra).

    I have added some more hyperlinks to the entry, in the first paragraphs.

    Regarding the entry title: a more canonical title choice might be “Cole spectrum” or maybe “spectrum of a model over a geometric theory” or the like.

    • CommentRowNumber6.
    • CommentAuthorThomas Holder
    • CommentTimeOct 11th 2014

    I have no problems with renaming as the title is a bit heavy. I was kind of afraid that ’Cole spectrum’ suggests for one thing too much a concrete spectrum for some particular algebraic theory and too established a term, but I sure can live with it. Maybe something like ’Cole spectra’ could be an alternative. Given that these words appear in Cole’s title they are probably good search-engineering. So whoever has a clear preference should go ahead and rename!