Well-Pointed Coalgebras
Logic in Computer Science
2015-07-01 v3 Category Theory
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.
Cite
@article{arxiv.1305.0576,
title = {Well-Pointed Coalgebras},
author = {Jiří Adámek and Stefan Milius and Lawrence S Moss and Lurdes Sousa},
journal= {arXiv preprint arXiv:1305.0576},
year = {2015}
}