# Interacting Hopf monoids and Graphical Linear Algebra

### APA

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

### MLA

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

### BibTex

@misc{ pirsa_PIRSA:17080007, doi = {10.48660/17080007}, url = {https://pirsa.org/17080007}, author = {Sobocinski, Pawel}, keywords = {Quantum Foundations, Quantum Information}, language = {en}, title = {Interacting Hopf monoids and Graphical Linear Algebra}, publisher = {Perimeter Institute}, year = {2017}, month = {aug}, note = {PIRSA:17080007 see, \url{https://pirsa.org}} }

University of Southampton

Talk Type

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.