Lambda the Ultimate

inactiveTopic Abramsky powerdomain
started 12/30/2001; 6:11:14 PM - last post 1/5/2002; 4:42:44 AM
Igor - Abramsky powerdomain  blueArrow
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 cpo-algebras with strict homomorphism be extended into an adjunction between CPO with continuous maps and its category of cpo-algebras? 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  blueArrow
1/2/2002; 4:32:57 PM (reads: 853, responses: 0)
What do you mean by cpo-algebra? 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 F-algebras and F-homomorphisms 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  blueArrow
1/5/2002; 4:42:44 AM (reads: 846, responses: 0)
I am sorry: I must admit that my question was not clear. By cpo-algebra, I ment sigma-algebra 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 F-U 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.