🚀 go-pugleaf

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