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.
Bonchi F., Sobocinski P., Zanasi F. (2017). Interacting Hopf algebras. JOURNAL OF PURE AND APPLIED ALGEBRA, 221(1), 144-184 [10.1016/j.jpaa.2016.06.002].
Interacting Hopf algebras
Zanasi F.
2017
Abstract
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.File in questo prodotto:
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