Well-Pointed Coalgebras (Extended Abstract)

  • Jiří Adámek
  • Stefan Milius
  • Lawrence S. Moss
  • Lurdes Sousa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7213)


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.


Binary Tree Inverse Image Full Subcategory Regular Language Label Transition System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jiří Adámek
    • 1
  • Stefan Milius
    • 1
  • Lawrence S. Moss
    • 2
  • Lurdes Sousa
    • 3
  1. 1.Institut für Theoretische InformatikTechnische Universität BraunschweigGermany
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA
  3. 3.Departamento de MatemáticaInstituto Politécnico de ViseuPortugal

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