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).

nLab > Latest Changes: stereotype space

Bottom of Page

1 to 9 of 9

  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 9th 2013

    Someone anonymously started stereotype space. How well-used is this notion?

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 9th 2013

    It’s the first I’d heard of it (which might not mean much). But I have to say that it does look very interesting, and I’m glad the Anonymous Coward wrote something (even if it’s just a copy and paste from Wikipedia).

    • CommentRowNumber3.
    • CommentAuthorYemon Choi
    • CommentTimeNov 10th 2013

    Promoted by Sergei Akbarov in recent years, IIRC. Am a bit busy right now but someone could probably dig up the title, if not the content, of his relevant articles through MRLookup

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 10th 2013

    I’ve added more material to stereotype space. A main result (hinted at but not quite said in the Wikipedia article) is that stereotype spaces form a star-autonomous category. (It’s amazing to me how people keep rediscovering this concept in disparate areas, without realizing that categorists have had the general notion for 35 years.)

    • CommentRowNumber5.
    • CommentAuthorYemon Choi
    • CommentTimeNov 10th 2013

    Wasn’t Michael Barr motivated by the existing theorems in functional analysis, in particular the Mackey topology on the dual of a TVS? I haven’t read his paper(s) properly and when I did it was some time ago.

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 10th 2013

    Indeed, that is my understanding as well, Yemon. So clearly I’m not trying to lord the category theorists over the functional analysts; I was suggesting that perhaps some of the functional analysts aren’t aware of the abstract niches that have been developed starting from those theorems. Or is that unfair?

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeNov 10th 2013

    I thought something with this property was called “reflexive”.

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 10th 2013

    Mike, yes I guess that is so, except that I’m not sure if “reflexive” is reserved for a particular sense of “dual”. So I’ll hold off adding that in.

    • CommentRowNumber9.
    • CommentAuthortrent
    • CommentTimeApr 10th 2016

    just came across akbarov’s work via his extremely interesting recent mathoverflow answer:

    Recently a new application of functional analysis in geometry appeared, the study of envelopes of topological algebras. It allows to look at “big” geometric disciplines – complex geometry, differential geometry, topology – from the point of view of category theory, so that these disciplines become “purely categorical constructions”. This can be considered as a developement of Klein’s Erlangen program.

    According to this view, different geometric disciplines are just pictures that appear in the imagination of an outlooker after applying different “observation tools” for studying a given category of topological algebras. Formally, this “projection of functional analysis to geometry” is established by a categorical construction, called envelope (and there are many different envelopes that give different geometries as disciplines).

    This activity allows to build different generalizations of Pontryagin duality to classes of non-commutative groups (including some quantum groups).

    checked the nlab/nforum and this is the only page that mentions him. is his work well known at all in 2016? fairly obscure?

1 to 9 of 9

  1.