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Stark's reply re regular subobjects in CCCPO
Date: Thu, 6 Aug 92 16:15:40 -0400
(Gene Stark, when responding to Alan Jeffrey and Edmond Robinson's
question on Regular subobjects in CCCPO, writes:
>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. )
Many such categories have been considered by people for
domain theoretic models of linear logic
(symmetric monoidal closed categories):
* Of course Girard's coherent spaces uses these kind of maps,
which are linear, stable functions under Berry order.
* Vaughan Pratt's work on Event Spaces and Their Linear Logic,
uses certain join preserving functions as morphisms (under the
extensional order).
* My MFPS paper (LNCS 598, pp426-435) gives a monoidal closed category
of stable event structures with linear maps. These corresponds to
the category of dI-domains and linear, stable functions, under the
Berry order.
* The journal version (to appear in MSCS) of the above paper
contains a description of the linear category of prime algebraic
lattices with linear functions under the extensional order.
* The category of prime algebraic lattices with linear functions
has also been extensively studied by Michael Huth (KSU-report),
as a maximal monoidal closed category inside the category of
bounded complete cpos.
* Raymond Hoofman's recent thesis on Non-Stable Models of linear
logic uses extensively linear functions as morphisms.
* I just finished a paper on quasi-linear functions, a generalization
of the notion of linear functions. The title of the paper is
`Quasi-Prime Algebraic Domains: A Linear Category of Non-Linear Functions'
which is available on request.
-- Guo-Qiang Zhang