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    Hasegawa, Masahito 2014. Denotational Semantics and Quantum Topology. Electronic Proceedings in Theoretical Computer Science, Vol. 172,

    Mellies, Paul-Andre 2012. 2012 27th Annual IEEE Symposium on Logic in Computer Science. p. 481.

  • Mathematical Structures in Computer Science, Volume 22, Issue 4
  • August 2012, pp. 618-650

A quantum double construction in Rel

  • DOI:
  • Published online: 18 May 2012

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.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
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