This paper proposes a categorical foundation for composing multi-resource in manufacturing systems. The composing procedures of overall system can be explained by pushout of category theory. The purpose of this paper is to resolve the issue involves in resource sharing, coordination and conflict for modeling the distributed manufacturing systems. We will propose a method for modeling discrete event system. The mathematical foundation lies in assuring that the constructed models have mathematical properties, e.g. consistency and completeness, and overcome the drawbacks of traditional function models, since it can show not only the static structure of resources but also the behavioral semantics of resources. The categorical notations and properties are to be expressed by a workcell example.