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Topical categories of domains

Published online by Cambridge University Press:  01 October 1999

STEVEN VICKERS
STEVEN VICKERS
Affiliation:
Department of Computing, Imperial College, 180 Queen's Gate, London SW7 2BZ, England. Email: s.vickers@doc.ic.ac.uk
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Abstract

This paper shows how it is possible to express many techniques of categorical domain theory in the general context of topical categories (where ‘topical’ means internal in the category Top of Grothendieck toposes with geometric morphisms). The underlying topos machinery is hidden by using a geometric form of constructive mathematics, which enables toposes as ‘generalized topological spaces’ to be treated in a transparently spatial way, and also shows the constructivity of the arguments. The theory of strongly algebraic (SFP) domains is given as a case study in which the topical category is Cartesian closed.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 9 , Issue 5 , October 1999 , pp. 569 - 616
Copyright
1999 Cambridge University Press

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