Tags:cartesian monoidal category, coalgebra, controlled stochastic process, dataflow programming, feedback, final coalgebra, markov category, monoidal category, monoidal stream, signal flow graph, stochastic process, stream, string diagram and symmetric monoidal category
Abstract:
We introduce monoidal streams: a generalization of synchronous stream processes to monoidal categories. Monoidal streams over a symmetric monoidal category form a feedback monoidal category. In the same way that classical streams provide semantics to dataflow programming with pure functions; monoidal streams provide semantics to dataflow programming where theories of processes are represented by a symmetric monoidal category. As an example, we study a stochastic dataflow language.