Nominal String Diagrams
Logic in Computer Science
2019-04-17 v1
Abstract
We introduce nominal string diagrams as, string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we develop the beginnings of a theory of monoidal categories internal in a symmetric monoidal category. As an instance, we obtain a notion of a nominal PROP as a PROP internal in nominal sets. A 2-dimensional calculus of simultaneous substitutions is an application.
Keywords
Cite
@article{arxiv.1904.07534,
title = {Nominal String Diagrams},
author = {Samuel Balco and Alexander Kurz},
journal= {arXiv preprint arXiv:1904.07534},
year = {2019}
}