Geometrical product specifications (GPS) is a standard system defined by ISO/TC213 which covers the standardization for micro-and macro-geometry specifications to make it suitable for the requirements of modern technologies. In addition, it integrates specifications and verification to make geometrical specifications more unambiguous and unique. Data modeling is a primary task in building an integrated information system for the application of geometrical characteristics consistent with the GPS standard system. It is feasible to extend this data modeling method to the whole GPS information system. This paper presents data modeling for the integration between specifications and verification for cylindricity consistent with GPS based on the category theory. The categorical data modeling method represents and stores all the elements and the relationships between them concerning the specifications and the verification process for cylindricity by categories, objects and morphisms; the established categories can be extended flexibly; the relationships between the objects were refined by pull back structures; and the manipulations of the model, such as query and the closure of query, are realized successfully by functor transforms in category theory.