Recursive coalgebras of finitary functors

Abstract For finitary set functors preserving inverse images several concepts of coalgebras A are proved to be equivalent: (i) A has a homomorphism into the initial algebra, (ii) A is recursive, i.e., A has a unique coalgebra-to-algebra morphism into any algebra, and (iii) A is parametrically recursive. And all these properties mean that the system described by A always halts in finitely many steps.

• Type: Journal
• Year: 2007
• Where: ITA
• Authors: Jirí Adámek, Dominik Lücke, Stefan Milius
• Keywords: Communications, Initial Algebra, Inverse Images, ITA 2007, Unique Coalgebra-to-algebra Morphism