Interacting Hopf Algebras

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.

References in corpus (4)

• The ZX-calculus is incomplete for quantum mechanics
• The ZX-calculus is complete for the single-qubit Clifford+T group
• Connector algebras for C/E and P/T nets' interactions
• Interacting Hopf Algebras: the theory of linear systems

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