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 comma 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 finite 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 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.
    • CommentAuthorMike Shulman
    • CommentTimeOct 20th 2017
    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeOct 20th 2017

    I’d like to write something about non-symmetric *\ast-autonomous categories, but I can’t decide whether it should go at star-autonomous category (which is presently only about the symmetric version) or on its own page. Any thoughts?

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 20th 2017

    Is it that in the literature people generally say *\ast-autonomous category and intend the symmetric case? Then there’s annoying ’not necessarily symmetric’ kind of qualification. Isn’t it better to let the general term win out, then specify ’symmetric’?

    If the latter, is there enough material to split pages, or could the symmetric case just feature in a subsection?

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeOct 20th 2017

    Well, I think it’s more that the original notion was symmetric, with the non-symmetric case introduced rather later. My impression (although I’m not an expert in this field) is that recently people have been pushing to make the general term win out, as you say. But whoever wrote our page chose to talk only about the symmetric case, so I didn’t want to unilaterally make the change in case they had a good reason for that choice.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 20th 2017

    I’m not sure it was really a ’choice’, in the sense that the author held the symmetric notion in one hand and the non-symmetric one in the other, and then weighed in favor of the symmetric notion. As far as I know, the symmetric notion has been studied much more (for example, from the perspective of studying coherence problems, I’m much more at home with the symmetric notion).

    I for one have no objection to making adjustments to the page to redress this. But once one has the non-symmetric notion, it seems one is invited to ’oidify’ (horizontally categorify); has an appropriate 2-dimensional notion been considered in the literature?

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeOct 20th 2017

    it seems one is invited to ’oidify’ (horizontally categorify)

    That’s the name of this thread: linear bicategory. (-:

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeOct 20th 2017

    (Or, more precisely, a linear bicategory with linear adjoints for all morphisms.)

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 20th 2017

    Re #6: oh, so it is! Helps to look at the thread title now and then. :-)

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeOct 20th 2017

    Well, it’s partly my fault for taking the thread in a different (though related) direction in #2.