🚀 go-pugleaf

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