Architectures depict design principles: paradigms that can be understood by all, allow thinking on a higher plane and avoiding low-level mistakes. They provide means for ensuring correctness by construction by enforcing global properties characterizing the coordination between components. An architecture can be considered as an operator A that, applied to a set of components B, builds a composite component A(B) meeting a characteristic property Φ. Architecture composability is a basic and common problem faced by system designers. In this paper, we propose a formal and general framework for architecture composability based on an associative, commutative and idempotent architecture composition operator ‘⊕’. The main result is that if two architectures A1 and A2 enforce respectively safety properties Φ1 and Φ2, the architecture A1 ⊕ A2 enforces the property Φ1 & Φ2, that is both properties are preserved by architecture composition. We also establish preservation of liveness properties by architecture composition. The presented results are illustrated by a running example and a case study.