Recursive data types in algebraically \(\omega\)-complete categories. (English) Zbl 0841.18003
A connection between the notions of “algebraically complete” and “algebraically compact” category is considered. The notions were introduced by P. Freyd. In the first case, every functor should have a least fixpoint, and in the second, a least and the largest fixpoint, that canonically coincide. It is shown that 1) several interesting categories are algebraically \(\omega\)-complete and 2) categories enriched over complete partial orders are “almost” \(\omega\)-compact: each localy-continuous functor has a canonical fixpoint.
Reviewer: S.V.Solov’ev (Aarhus)
MSC:
18B20 | Categories of machines, automata |
68Q65 | Abstract data types; algebraic specification |
68P05 | Data structures |
18A35 | Categories admitting limits (complete categories), functors preserving limits, completions |