A categorical generalization of Scott domains

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.