Adámek, Jiří and Milius, Stefan and Moss, Lawrence S and Sousa, Lurdes - Well-Pointed Coalgebras

lmcs:704 - Logical Methods in Computer Science, August 9, 2013, Volume 9, Issue 3
Well-Pointed Coalgebras

Authors: Adámek, Jiří and Milius, Stefan and Moss, Lawrence S and Sousa, Lurdes

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.


Source : oai:arXiv.org:1305.0576
DOI : 10.2168/LMCS-9(3:2)2013
Volume: Volume 9, Issue 3
Published on: August 9, 2013
Submitted on: July 31, 2012
Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory


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