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

lmcs:704 - Logical Methods in Computer Science, August 9, 2013, Volume 9, Issue 3 - https://doi.org/10.2168/LMCS-9(3:2)2013
Well-Pointed Coalgebras

Authors: Jiří Adámek ; Stefan Milius ; Lawrence S Moss ; Lurdes Sousa

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.


Volume: Volume 9, Issue 3
Published on: August 9, 2013
Accepted on: June 25, 2015
Submitted on: July 31, 2012
Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory


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