Samson Abramsky, Richard Blute, and Prakash Panangaden \Nuclear and trace ideals in tensored -categories", preprint, 1997. To appear in the special issue of Journal of Pure and Applied Algebra in honour of Prof. Michael Barr.  Home/Search   Document Not in Database   Summary   Related Articles

....notion of feedback in stream processing , where one delays the output until the next time step when one uses it as input: for streams, feedback on the switch is delay. It should also be mentioned that a notion of feedback which is speci c to certain maps (not just objects) is also possible, see [ABP97]. There the authors introduce the notion of a trace ideal. The motivating example is in the category of Hilbert spaces: while many morphisms do not have a trace, within each Hom(H;H) there is a subspace of morphisms which can be traced. This subspace forms a two sided ideal which is closely ....

....superposing requirements, and yanking: tightening and superposing are structural axioms which express no more than the strength of the combinator; yanking, however, is a distinct requirement which makes the operator a trace rather than a general feedback combinator. Remark 8 (Trace ideals) In [ABP97], the authors introduce the notion of a trace ideal, a notion which models the fact that in (for example) Hilbert spaces one has many maps without a trace, in particular identity morphisms generally do not have traces. We can model this phenomenon in our setting by allowing tr U to be a partial ....

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Samson Abramsky, Richard Blute, and Prakash Panangaden \Nuclear and trace ideals in tensored -categories", preprint, 1997. To appear in the special issue of Journal of Pure and Applied Algebra in honour of Prof. Michael Barr.

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