Abstract
In this paper we develop a natural powerobject construction in the context of enriched categories, a context which generalizes the traditional order-theoretic and metric space contexts. This powerobject construction is a subobject transformer involving the dialectical flow of closed subobjects of enriched categories. It is defined via factorization of a comprehension schema over metrical predicates, followed by the fibrational inverse image of metrical predicates along character, the left adjoint in the comprehension schema. A fundamental continuity property of this metrical powerobject construction vis-a-vis greatest fixpoints is established by showing that it preserves the limit of any Cauchy ωop-diagram. Using this powerobject construction we unify two well-known fixpoint semantics for concurrent interacting processes.
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© 1988 Springer-Verlag Berlin Heidelberg
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Kent, R.E. (1988). The metric closure powerspace construction. In: Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Language Semantics. MFPS 1987. Lecture Notes in Computer Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19020-1_9
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DOI: https://doi.org/10.1007/3-540-19020-1_9
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