This is the first part of the first report in a series devoted to exploring the interface or "junction" between computer science and category theory. We expect that both will benefit from the exploration: computer science by a powerful set of tools and a general methodology providing a rigorous and uniform approach to many of its basic concepts, methods, and questions; and category theory by a nontrivial collection of practical applications and illustrations, plus a number of new problems and results. Our present general purposes are to provide a clear, leisurely, and well-illustrated introduction to the basic language of category theory, and to give introductory formulations of some of the computer science topics we treat later in greater depth, including machines, automata, and languagea. Later reports will contain the research results which led us to undertake this series.
Section 0 contains a general introduction, a discussion of the special relevance of category theory to computer science, and intuitive interpretations for the key categerical concepts. Section 1 contains a compendium of the background definitions and notation assumed in subsequent sections, especially oriented toward our computer application and category theoretic viewpoint. Section 2 contains the two most basic definitions, of category and functor. There are many examples and frequent intuitive discussions.
By: J. A. Goguen, J. W. Thatcher, E. G. Wagner, J. B. Wright
Published in: RC4526 in 1973
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