The monad of diagrams as a mathematical metamodel of systems engineering

The paper addresses issues associated with the development of advanced mathematical methods for systems engineering suitable as the basis of computer tools for automatic synthesis and analysis of systems and processes. Following recent trends, category theory is employed as the framework for the methods. Its application is based on representing the structure of systems, processes, requirements, and other system design results as diagrams in categories whose objects are the algebraic models of parts and morphisms describe relationships between parts. Applying the fundamental Grothendieck flattening construction, the following constructions are described explicitly: categories of diagrams, the monad of diagrams, and the monad and the comonad of pointed diagrams. Application areas of these constructions in systems engineering procedures are identified. An approach is proposed to implement highly automated technologies of the generative design kind for complex multilevel systems.