Methods of the category theory in digital design of heterogeneous cyber-physical systems

A mathematical device built upon the category theory is developed which was previously proposed to formally describe and rigorously explore engineering procedures based on mathematical and computer modeling. With the help of the device, highly automated procedures for designing heterogeneous cyber-physical systems on top of digital twins, demanded by the upcoming fourth industrial revolution, are described and explored. For this purpose, the novel construction of the multicomma category is introduced, whose objects are the architectural models of a heterogeneous cyber-physical system with a certain fixed structural hierarchy scheme represented from a certain architecture viewpoint, and morphisms describe actions associated with selection of constituents for assembling a system from them. The application of the multicomma category in solving direct and inverse problems of designing individual systems and complex systems of systems is considered.