Well-Pointed coalgebras (extended abstract)

Authors:
Jiří Adámek;Stefan Milius;Lawrence S. Moss;Lurdes Sousa
Affiliations:
Institut für Theoretische Informatik, Technische Universität Braunschweig, Germany;Institut für Theoretische Informatik, Technische Universität Braunschweig, Germany;Department of Mathematics, Indiana University, Bloomington, IN;Departamento de Matemática, Instituto Politécnico de Viseu, Portugal
Venue:
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Year:
2012

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Abstract

For set functors preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. And the initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Taylor [16]. Finally, the initial iterative algebra consists of all finite well-pointed coalgebras. Numerous examples are discussed e.g. automata, graphs, and labeled transition systems.