Abstract
After a brief historical review of early attempts to apply category theory to place sequential machines and control systems in a unified framework, we present three contributions to the theory of machines in a category: the dynamical interpretation functor which relates the response of a machine to a sequence of inputs with the reachability map in the system category; an application of the Krull-Schmidt theorem to provide a parallel decomposition for machines with polynomial state-transition; and a generalized notion of Hankel matrix which enables one to present finiteness conditions for linear systems even when defined over noncommutative rings, and for certain classes of nonlinear systems characterized by adjoint functors.
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