This paper proposes a categorical foundation for integrating various types of manufacturing knowledge 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 sharing and coordination for modeling knowledge application in 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 but also the dynamic semantics. The categorical notations and properties are expressed by an example of flexible assembly workcell.