17080007

Video URL

http://pirsa.org/17080007

Interacting Hopf monoids and Graphical Linear Algebra

Sobocinski, P. (2017). Interacting Hopf monoids and Graphical Linear Algebra. Perimeter Institute for Theoretical Physics. http://pirsa.org/17080007

Sobocinski, Pawel. Interacting Hopf monoids and Graphical Linear Algebra. Perimeter Institute for Theoretical Physics, Aug. 02, 2017, http://pirsa.org/17080007 

          @misc{ scitalks_17080007,
            doi = {},
            url = {http://pirsa.org/17080007},
            author = {Sobocinski, Pawel},
            keywords = {Quantum Foundations, Quantum Information},
            language = {en},
            title = {Interacting Hopf monoids and Graphical Linear Algebra},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2017},
            month = {aug},
            note = {17080007 see, \url{https://scitalks.ca/PIRSA/17080007}}
          }

Pawel Sobocinski University of Southampton

Source Repository PIRSA
Collection
Talk Type Conference
Subject

Abstract

The interaction of Hopf monoids and Frobenius monoids is the productive nucleus of the ZX calculus, where famously each Frobenius monoid-comonoid pair corresponds to a complementary basis and the Hopf structure describes the interaction between the bases. The theory of Interacting Hopf monoids (IH), introduced by Bonchi, Sobocinski and Zanasi, features essentially the same Hopf-Frobenius interaction pattern. The free symmetric monoidal category generated by IH is isomorphic to the category of linear relations over the field of rationals: thus the string diagrams of IH are an alternative graphical language for elementary concepts of linear algebra. IH has a modular construction via distibutive laws of props, and has been applied as a compositional language of signal flow graphs. In this talk I will outline the equational theory, its construction and applications, as well as report on ongoing and future work.