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Dynamical Systems and Sheaves
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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 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.
Forward citations
Cited by 2 Pith papers
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A compositional framework for open classical kinematic systems
Open kinematic systems are modeled as morphisms in a category Kin(F), and universal joints and sliding hinges are proved to require at least three actors, hence are not lower kinematic pairs.
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Dynamical Systems as Functorial Realisations of Abstract Evolution Shapes
A categorical framework defines dynamical systems as functors from abstract evolution shapes to coefficient categories, with convergence and Lyapunov stability expressed through cosieve filters and sublevel neighbourhoods.
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