Abstract. A mathematical semantics is proposed for the notion of architectural connector, in the style defined by Allen and Garlan, that builds on Goguen’s categorical approach to General Systems Theory and other algebraic approaches to specification, concurrency, and parallel program design. This semantics is, essentially, ADL-independent, setting up criteria against which formalisms can be evaluated according to the support that they provide for architectural design. In particular, it clarifies the role that the separation between computation and coordination plays in supporting architecture-driven approaches to software construction and evolution. It also leads to useful generalisations of the notion of connector, namely through the use of multiple formalisms in the definition of the glue and the roles, and their instantiations with programs or system components that can be implemented in different languages or correspond to "real-world" components.