A categorical generalization of Scott domains

Authors:
Jiří Adámek
Affiliations:
Technical University of Braunschweig, P.O. Box 3329, 38023 Braunschweig, Germany. Email: adamek@iti.cs.tu-bs.de
Venue:
Mathematical Structures in Computer Science
Year:
1997

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Abstract

Algebraic CPOs naturally generalize to finitely accessible categories, and Scott domains (i.e., consistently complete algebraic CPOs) then correspond to what we call Scott-complete categories: finitely accessible, consistently (co-)complete categories. We prove that the category SCC of all Scott-complete categories and all continuous functors is cartesian closed and provides fixed points for a large collection of endofunctors. Thus, SCC can serve as a basis for semantics of computer languages.