Algebraically Compact Categories I read Freyd's paper "Algebraically Complete Categories" in the famous Como90 and I have two questions about the notion of algebraic compactness he defined in that paper. (If you are not familiar with the definition, here it is: A category is called algebraically compact if every endofunctor has an initial algebra and a final co-algebra which are canonically isomorphic.)


What are some examples of algebraically compact categories? Freyd mentions an example but strictly speaking the condition in the definition holds only for certain endofunctors of interest. From reading other papers (such as "Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire") I guess that category of cpo's, omega-cpo's or categories enriched over (omega-) cpo's are algebraically compact. What is the standard reference for this fact?
Freyd says that the definition is motivated by the "principal of versality" and, being a nonnative speaker of English, I am confused. First of all, I think it should be principle, not principal. Also what is versality? Does he mean versatility? Is this a game on words like (uni)versality?
I found the reference for CPO-like categories.
Scott's paper Continuous Lattices in the book Toposes, Algebraic Geometry and Logic. It is explained in the comments right after corollary 4.3.
A more general theorem can be found in Smyth's and Plotkin's paper Category-Theoretic Solution of Recursive Domain Equations. It is lemma 2.

However, again, the functors are not arbitrary. One needs some sort of a continuity assumption.