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Abstract

“Information systems” have been introduced by Dana Scott as a convenient means of presenting a certain class of domains of computation, usually known as Scott domains. Essentially the same idea has been developed, if less systematically, by various authors in connection with other classes of domains. In previous work, the present authors introduced the notion of anI-category as an abstraction and enhancement of this idea, with emphasis on the solution ofdomain equations of the formD ≅F(D), withF a functor. An important feature of the work is that we arenot confined to domains of computation as usually understood; other classes of spaces, more familiar to mathematicians in general, become also accessible. Here we present the idea in terms of what we callinformation categories, which are concrete I-categories in which the objects are structured sets of “tokens” and morphisms are relations between tokens. This is more in the spirit of information system work, and enables more specific results to be obtained. Following an account of the general theory, several examples are discussed in some detail: Stone spaces (as an “ordinary” mathematical example), Scott domains, SFP domains, and continuous bounded complete domains.

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  1. Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen's Gate, SW7 2BZ, London, England

    Abbas Edalat & Michael B. Smyth

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  1. Abbas Edalat
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  2. Michael B. Smyth
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Edalat, A., Smyth, M.B. Information categories. Appl Categor Struct 1, 197–232 (1993). https://doi.org/10.1007/BF00880044

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