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Communication Dans Un Congrès Lecture Notes in Computer Science Année : 2014

Interacting Bialgebras are Frobenius

Résumé

Bialgebras and Frobenius algebras are different ways in which monoids and comonoids interact as part of the same theory. Such theories feature in many fields: e.g. quantum computing, compositional semantics of concurrency, network algebra and component-based programming. In this paper we study an important sub-theory of Coecke and Duncan's ZX-calculus, related to strongly-complementary observables, where two Frobenius algebras interact. We characterize its free model as a category of ℤ2-vector subspaces. Moreover, we use the framework of PROPs to exhibit the modular structure of its algebra via a universal construction involving span and cospan categories of ℤ2-matrices and distributive laws between PROPs. Our approach demonstrates that the Frobenius structures result from the interaction of bialgebras.
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Dates et versions

hal-00989174 , version 1 (09-05-2014)

Identifiants

  • HAL Id : hal-00989174 , version 1

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Filippo Bonchi, Pawel Sobocinski, Fabio Zanasi. Interacting Bialgebras are Frobenius. FoSSaCS 2014, Apr 2014, Grenoble, France. pp.351-365. ⟨hal-00989174⟩
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