Dynamical Systems and Sheaves
Abstract
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special cases include continuous and discrete dynamical systems (e.g. Moore machines). Additionally, morphisms between the different types of systems allow their translation in a common framework. A central goal is to understand the systems that result from arbitrary interconnection of component subsystems, possibly of different types, as well as establish conditions that ensure totality and determinism compositionally. The fundamental categorical tools used here include lax monoidal functors, which provide a language of compositionality, as well as sheaf theory, which flexibly captures the crucial notion of time.
Cite
@article{arxiv.1609.08086,
title = {Dynamical Systems and Sheaves},
author = {Patrick Schultz and David I. Spivak and Christina Vasilakopoulou},
journal= {arXiv preprint arXiv:1609.08086},
year = {2019}
}
Comments
59 pages (appendix removed); numerous revisions suggested by anonymous referee, final version to appear in `Applied Categorical Structures'