Propification and the Scalable Comonad
Category Theory
2022-05-17 v1 Quantum Physics
Abstract
String diagrams can nicely express numerous computations in symmetric strict monoidal categories (SSMC). To be entirely exact, this is only true for props: the SSMCs whose monoid of objects are free. In this paper, we show a propification theorem asserting that any SSMC is monoidally equivalent to a coloured prop. As a consequence, all SSMCs are within reach of diagrammatical methods. We introduce a diagrammatical calculus of bureaucracy isomorphisms, allowing us to handle graphically non-free monoids of objects. We also connect this construction with the scalable notations previously introduced to tackle large-scale diagrammatic reasoning.
Keywords
Cite
@article{arxiv.2205.07760,
title = {Propification and the Scalable Comonad},
author = {Titouan Carette},
journal= {arXiv preprint arXiv:2205.07760},
year = {2022}
}