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 limit 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 subobject 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.
    • CommentAuthorFinnLawler
    • CommentTimeMay 13th 2011

    Just a quick question, in case anyone can tell me off hand (before I go scouring the literature): does the Gray tensor product make the category of strict 2-categories and pseudofunctors into a monoidal closed category? If so, is there a name for categories enriched in this category?

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeMay 14th 2011

    I haven’t seen this written down, I don’t think, or checked the details, but I’d be surprised if it weren’t monoidal and I’d be surprised if it were closed. For instance, since 1 is the unit for the Gray tensor product, you’d have a bijection between pseudofunctors ABA\to B and pseudofunctors 1Hom(A,B)1\to Hom(A,B). But the latter is not just an object of Hom(A,B)Hom(A,B) but an automorphism in it coherently isomorphic to the identity. So I don’t see a natural candidate for Hom(A,B)Hom(A,B).

    • CommentRowNumber3.
    • CommentAuthorFinnLawler
    • CommentTimeMay 19th 2011

    Thanks for that, Mike. I thought I might need this to define some sort of 3-category of biprofunctors, but I don’t think it works. (It seems Biprof is best defined just as a subtricategory of Bicat.)