METHODS OF CATEGORY THEORY IN MODEL-BASED SYSTEMS ENGINEERING
A mathematical device based on the category theory is proposed to formally describe and rigorously explore procedures of employing models in engineering that constitute the contents of model-based systems engineering (MBSE). 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. The soundness of the device is justified on the basis of standards that govern description of the systems’ structure such as IEC 81346. Category-theoretical methods for solving a number of practical problems of assembling systems are proposed and explored. Examples of solving such problems are provided in categories that represent two key application areas for MBSE: geometric modeling of complex shapes and discrete-event simulation of the behavior of industrial systems.