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arxiv: 1403.7048 · v4 · pith:RWKYDTFYnew · submitted 2014-03-27 · 💻 cs.LO · math.CT

Interacting Hopf Algebras

Filippo Bonchi , Pawel Sobocinski , Fabio Zanasi This is my paper
classification 💻 cs.LO math.CT
keywords hopfalgebraalgebrasinteractingapproachaxiomscomposingconstruction
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We introduce the theory IH of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IH are derived using Lack's approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid-comonoid pairs. This construction is instrumental in showing that IH is isomorphic to the PROP of linear relations (i.e. subspaces) over the field of fractions of R.

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