Clock systems for stochastic and non-deterministic categorical systems theories
Category Theory
2026-04-03 v2
Abstract
One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form a representable covariant functor to Set. And more generally, in the compositional setting, behaviors form a representable double functor to Span. Clock systems are convenient because behavior functors represented by clock systems are automatically well-behaved. It was previously not known whether stochastic and non-deterministic systems theories have clock systems. In this paper, we show that indeed they do have clock systems. Moreover, the clock systems for non-deterministic systems point to generalized notions of behavior for non-linear time.
Cite
@article{arxiv.2603.29573,
title = {Clock systems for stochastic and non-deterministic categorical systems theories},
author = {Owen Lynch and David Jaz Myers and Eigil Fjeldgren Rischel and Sam Staton},
journal= {arXiv preprint arXiv:2603.29573},
year = {2026}
}