Inner and Mutual Compatibility of Basic Operations on Module Specifications

The category Mod of module specifications and module morphisms is introduced and used to show the inner compatibilities of union, composition and actualization of module specifications. Using algebraic techniques, we can provide a simple proof of the compatibility of actualization and union (i.e. that the union of actualized modules is an appropriate actualization of a union of the modules) and establish the compatibility of composition with parameterized actualization (i.e., that an actualization of the composite M1·M2 can be obtained as a composition of the actualized modules M1 and M2).