Category theory as a mathematical pragmatics of model-based systems engineering

Mathematical device built upon the category theory is developed which was previously proposed to formally describe and rigorously explore procedures of employing models in engineering that constitute the pragmatics of model-based systems engineering. The essence of the device consists in mathematical representation of assembly drawings (megamodels of systems) as diagrams in categories whose objects are models, and morphisms represent actions associated with assembling system models from component models. Category-theoretical methods for solving direct and inverse pragmatic problems of assembling systems are proposed and explored. The key role of the diagram monad is revealed. Special attention is paid to the problem of recovering the configuration of a given system, taking into account technological limitations of the assembling means and procedures. A number of key systems engineering concepts are matched with relevant constructions of the category theory.