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arxiv: 1305.0576 · v3 · pith:ZJPAGJH6new · submitted 2013-05-02 · 💻 cs.LO · math.CT

Well-Pointed Coalgebras

Ji\v{r}\'i Ad\'amek (Institut f\"ur Theoretische Informatik , Technische Universit\"at Braunschweig , Germany) , Stefan Milius (Institut f\"ur Theoretische Informatik , Technische Universit\"ut Braunschweig , Lawrence S Moss (Department of Mathematics , Indiana University , Bloomington
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IN USA) Lurdes Sousa (Polytechnic Institute of Viseu Centre for Mathematics of the University of Coimbra Portugal)
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classification 💻 cs.LO math.CT
keywords coalgebrasinitialwell-pointedalgebraconsistsfinalproperwell-founded
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For endofunctors of varieties 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. The initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Osius and Taylor. And initial algebras are precisely the final well-founded coalgebras. Finally, the initial iterative algebra consists of all finite well-pointed coalgebras. Numerous examples are discussed e.g. automata, graphs, and labeled transition systems.

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