Geometrical Product Specifications is an international standard system regarding standardization of dimensional,
tolerancing, surface texture and related metrological principles and practices in the charge of ISO/TC213. Integrated
information system is necessary to encapsulate the knowledge in GPS to extend its application in digital manufacturing.
Establishing a suitable data structure for GPS data is one of the main works in building the integrated information system.
This paper is focused on cylindricity and the main points are as follows: proposes the complete verification operator and
the complete drawing indication for cylindricity consistent with GPS standard system; models the inter/intra
relationships between the elements of operations involved in cylindricity and integrates them by category theory; solves
the storage format and closure of query for the categorical data model by the pull-back structure and functor transform in
category theory respectively.