Subject: Enrichment and Representation Theorems for Domains.

From: categories <[email-masked]>
Date: Tue, 28 Feb 1995 08:43:29 -0400 (AST)

Date: Mon, 26 Feb 1996 15:06:26 GMT
From: Marcelo Fiore <[email-masked]>

The prepint "Enrichment and Representation Theorems for Categories of 
Domains and Continuous Functions" is available from 
http://www.dcs.ed.ac.uk/home/mf files rep.dvi or rep.ps, or by 
anonymous ftp from ftp.dcs.ed.ac.uk directory pub/mf files rep.dvi or 
rep.ps.  

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               Enrichment and Representation Theorems 
         for Categories of Domains and Continuous Functions

                            Synopsis

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.
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