show/hide this revision's text 3 edited title

representing tensor-C^*-categories tensor-C*-categories in BIM
show/hide this revision's text 2 edited tags; added 100 characters in body

Given a factor M (=von Neumann alg. with center ℂ), let us write BIM for the ⊗-C*-category of M-M-bimodules.

Which ⊗-C*-categories can one faithfully embed into BIM?

⓵ Are there necessary conditions for a ⊗-C*-category to be representable in BIM?
⓶ Are there sufficient conditions for a ⊗-C*-category to be representable in BIM?

Comment:
I suspect that a lot is known about ⓶ in relation with the theory of planar algebras...
I specially care about ⓵: are there examples of ⊗-C*-categories that don't embed?
show/hide this revision's text 1

representing tensor-C^*-categories in BIM

Given a factor M (=von Neumann alg. with center ℂ), let us write BIM for the ⊗-C*-category of M-M-bimodules.

Which ⊗-C*-categories can one faithfully embed into BIM?

⓵ Are there necessary conditions for a ⊗-C*-category to be representable in BIM?
⓶ Are there sufficient conditions for a ⊗-C*-category to be representable in BIM?

Comment:
I suspect that a lot is known about ⓶ in relation with the theory of planar algebras...