Category theory is applied to the problem of representing heterogeneous software engineering technologies in a unified form suitable for their integration and coordination within the common software systems engineering cycle. Special attention is paid to modern technologies such as model-driven engineering and aspect-oriented programming. Universal category-theoretic semantic models of these technologies are constructed. A novel method of separation of concerns by explicating the aspectual structure of formal models of programs is proposed. We construct and analyze formal technologies (architecture schools) for designing technologies that comprise a mathematical basis for model-driven engineering.