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arXiv · 1305.0576

Well-Pointed Coalgebras

Jiří Adámek·Stefan Milius·Lawrence S Moss·Lurdes Sousa
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Abstract

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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Jiří Adámek, Stefan Milius, Lawrence S Moss, Lurdes Sousa. 2013-05-02. Well-Pointed Coalgebras. https://doi.org/10.2168/lmcs-9(3:2)2013

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