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Dynamical Systems and Sheaves

Dynamical Systems and Sheaves

Dynamical Systems and Sheaves

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Year:2016
Publisher:Autoedición
Pages:65 pages
Language:english
Since:06/10/2016
Size:498 KB
License:CC-BY

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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 discrete, continuous, and hybrid dynamical systems. A central goal is to understand the systems that result from arbitrary interconnection of component subsystems.

The fundamental categorical tools used here include lax functors out of monoidal categories, which provide a language of compositionality, as well as sheaf theory, which flexibly captures the crucial notion of time. Continuous- and discrete-time systems are related via functors, and a new sheaf-theoretic perspective on hybrid systems is proposed. A multitude of examples is offered in an appendix.

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