In this paper we show how by means of a categorical framework we can compose systems of concurrent object modules satisfying some interaction rules given by a specification. Module interaction can be either synchronous or asynchronous and both cases are considered separately. The behaviour of object modules is modelled by labelled prime event structures. The category of labelled prime event structures has (co)products. A product in the category of labelled prime event structures is given accordingly to Winskel and Nielsen but denotes parallel composition in a sense that does not have much practical interest. For synchronously communicating modules, by applying to the product a restriction on the allowed life cycles by means of the categorical concept of a functor induced by a cofibration and a morphism on labels, we achieve the desired joint behaviour.