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                Enrichment and Representation Theorems 
           for Categories of Domains and Continuous Functions
 by Marcelo P. Fiore, Dep't of Computer Science, LFCS, U. of Edinburgh 

  Domain-theoretic categories are axiomatised by means of categorical 
non-order-theoretic requirements on a cartesian closed category 
equipped with a commutative monad.  We prove an enrichment theorem 
showing that every axiomatic domain-theoretic category can be endowed 
with an intensional notion of approximation, the path relation, with 
respect to which the category Cpo-enriches. Subsequently, we provide a
representation theorem of the form: every small domain-theoretic 
category (with a lifting monad) has a full and faithful representation
in a domain-theoretic category of cpos and continuous functions (with a
lifting monad) in a suitable intuitionistic set theory.

  Our analysis suggests more liberal notions of domains.  In particular
we present a category where the path order is not omega-complete, but 
in which the constructions of domain theory (as, for example, the 
existence of uniform fixed-point operators and the solution of domain 
equations) are possible.

  This preprint is available from URL:
http://www.dcs.ed.ac.uk/home/mf
in the files rep.dvi and rep.ps.