2000 character limit reached
Interacting Hopf Algebras (1403.7048v4)
Published 27 Mar 2014 in cs.LO and math.CT
Abstract: 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.