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Regular subobjects in CCCPO
Date: Thu, 6 Aug 92 08:39:30 -0400
(Alan Jeffrey and Edmund Robinson give a characterization of regular subobjects
in the category of consistently complete cpos and strict, join-preserving maps,
and ask whether this result or similar ones are known in the community.)
In my papers:
``Compositional Relational Semantics for Indeterminate Dataflow Networks,''
Proceedings of Summer Conference on Category Theory and Computer Science,
Manchester, U.K., September, 1989, Springer LNCS 389, pp. 52-74.
``Connections Between a Concrete and an Abstract Model of Concurrent Systems,''
Proceedings of Fifth Conference on Mathematical Foundations of Program
Semantics, New Orleans, LA, Springer LNCS 442, pp. 53-79, March, 1989.
I showed the completeness of the subcategory of your CCCPO that
consists of the ``conflict event domains,'' which are finitary, algebraic,
consistently complete cpos that have some additional properties pertaining
to prime (covering) intervals. The morphisms are strict,
consistent-join-preserving maps that in addition preserve finite joins of
prime intervals. From the construction for equalizers given there, it is
clear that regular subobjects have the properties you state. Moreover,
a subobject satisfying these properties has a right adjoint with identity unit,
hence every regular subobject is a split coreflexive. (I get the impression
>from your posting that this is part of what is of interest to you.)
This is the first time I have heard of anyone else being interested in
categories of strict, consistent-join-preserving maps, and I am eager to hear
about anything else you find out.
- Gene Stark