Interacting Hopf Algebras

  title={Interacting Hopf Algebras},
  author={Filippo Bonchi and Pawel Sobocinski and Fabio Zanasi},
We introduce the theory IHR of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IHR 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 IHR is isomorphic to the PROP of linear relations (i.e. subspaces) over the field of fractions of R. 
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