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Abstract Systems and Sheaves

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We describe a categorical framework of modeling and analyzing systems in a broad sense. The latter can 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 and continuous dynamical systems. A central goal is to understand systems formed as arbitrary interconnections of component subsystems. This shall be accomplished using lax monoidal functors, which provide a coherent formalisation of systems, as well as sheaf theory, which captures the crucial notion of time.

This talk is part of the Category Theory Seminar series.

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