Interacting Hopf algebras
Copyright policy )Interacting Hopf algebras
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.
- University College London United Kingdom
- University of Southampton United Kingdom
- Radboud University Nijmegen Netherlands
- ENS de Lyon France
- University of Pisa Italy
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, Algebra and Number Theory, interacting Hopf algebras; IHR; PROP; Frobenius algebras, interacting Hopf algebras, Mathematics - Category Theory, spans and cospans of matrices, 510, Logic in Computer Science (cs.LO), monoid-comonoid pairs, Bialgebras, Monoidal, symmetric monoidal and braided categories, Frobenius algebra, Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.), FOS: Mathematics, equational theories, Category Theory (math.CT), Digital Security, PROP
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, Algebra and Number Theory, interacting Hopf algebras; IHR; PROP; Frobenius algebras, interacting Hopf algebras, Mathematics - Category Theory, spans and cospans of matrices, 510, Logic in Computer Science (cs.LO), monoid-comonoid pairs, Bialgebras, Monoidal, symmetric monoidal and braided categories, Frobenius algebra, Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.), FOS: Mathematics, equational theories, Category Theory (math.CT), Digital Security, PROP
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