A Mathematical Toolbox for the Software Architect

It is suggested that Category Theory provides the right level of mathematical abstraction to address languages for describing software architectures. Contrarily to most other formalisations of SA concepts, Category Theory does not promote any particular formalism for component and connector description but provides instead the very semantics of the concepts that are related to the gross modularisation of complex systems like "interconnection", "configuration", "instantiation" and "composition". Two examples, a category of programs for a parallel program design language and a category of temporal logic specifi cations, together with comparisons with other work, namely by Allen and Garlan, and Moriconi and Qian, are adduced to justify this claim.