Abramsky powerdomain
started 12/30/2001; 6:11:14 PM  last post 1/5/2002; 4:42:44 AM


Igor  Abramsky powerdomain
12/30/2001; 6:11:14 PM (reads: 804, responses: 2)


Can an adjunction between CPO with bottom and strict continuous maps and the category of its cpoalgebras with strict homomorphism be extended into an adjunction between CPO with continuous maps and its category of cpoalgebras?
If not, is it possible when the considered algebra is the Abramsky powerdomain? And is there in this case an adjunction between the same categories with bottom?


Frank Atanassow  Re: Abramsky powerdomain
1/2/2002; 4:32:57 PM (reads: 853, responses: 0)


What do you mean by cpoalgebra? Say C is a category of cpo's with bottom, and strict continuous maps, and F is an endofunctor on C. Do you mean simply the category of Falgebras and Fhomomorphisms in C, i.e., what is usually called Mod_C(F) or Alg_C(F)?
Well, I don't know the answer to this question anyway. You will probably have more success on the
types list, or the
categories list.


Igor  Re: Abramsky powerdomain
1/5/2002; 4:42:44 AM (reads: 846, responses: 0)


I am sorry: I must admit that my question was not clear.
By cpoalgebra, I ment sigmaalgebra with respect with some theory epsilon included in sigma*sigma, where sigma is a signature.
In fact, the answer to the first question seems to be no, since
if epsilon=void, bottom is not kept(see Abramsky: Domain theory). What I needed was to have an adjunction FU between CPO with bottom and the category of Abramsky powerdomains over CPO such that if f:A>UFB wath strict, then so was f*:UFA>UFB. This (which explains the last question) seems to hold (if I did not mistake).
Thank you for your advice.



