A categorical generalization of Scott domains. (English) Zbl 0884.18006

Adámek, Jiří

Math. Struct. Comput. Sci. 7, No. 5, 419-443 (1997).

Scott-complete categories are introduced as finitely accessible categories which are consistently cocomplete in the sense that every diagram with a cocone has a colimit. It generalizes Scott domains from posets to categories. It is shown that the category of Scott-complete categories and continuous functors is cartesian closed. Fixed points of endofunctors on it are studied as well.

Reviewer: J.Rosický (Brno)

MSC:

18B99	Special categories
68Q55	Semantics in the theory of computing
18D15	Closed categories (closed monoidal and Cartesian closed categories, etc.)
06B35	Continuous lattices and posets, applications

Keywords:

accessible category; Scott domain; fixed point; Scott-complete categories