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A quantum double construction in Rel†

Published online by Cambridge University Press:  18 May 2012

MASAHITO HASEGAWA
MASAHITO HASEGAWA*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan Email: [email protected]
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Abstract

We study bialgebras and Hopf algebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of bialgebras and Hopf algebras in Rel. In particular, for any group G, we derive a ribbon category of crossed G-sets as the category of modules of a Hopf algebra in Rel that is obtained by the quantum double construction. This category of crossed G-sets serves as a model of the braided variant of propositional linear logic.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 22 , Issue 4 , August 2012 , pp. 618 - 650
Copyright
Copyright © Cambridge University Press 2012

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