Interacting Hopf Algebras
Logic in Computer Science
2016-12-01 v4 Category Theory
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.
Cite
@article{arxiv.1403.7048,
title = {Interacting Hopf Algebras},
author = {Filippo Bonchi and Pawel Sobocinski and Fabio Zanasi},
journal= {arXiv preprint arXiv:1403.7048},
year = {2016}
}