Mathematical Structures in Computer Science

Research Article

A categorical manifesto

Joseph A. Goguena1

a1 Programming Research Group, University of Oxford, SRI International, Menlo Park CA, USA


This paper tries to explain why and how category theory is useful in computing science, by giving guidelines for applying seven basic categorical concepts: category, functor, natural transformation, limit, adjoint, colimit and comma category. Some examples, intuition, and references are given for each concept, but completeness is not attempted. Some additional categorical concepts and some suggestions for further research are also mentioned. The paper concludes with some philosophical discussion.

(Received August 06 1989)

(Revised August 14 1990)


† The research reported in this paper has been supported in part by grants from the Science and Engineering Research Council, the National Science Foundation, and the System Development Foundation, as well as contracts with the Office of Naval Research and the Fujitsu Corporation.