Covarieties of Coalgebras: Comonads and Coequations Export

@inproceedings{citeulike:565385, abstract = {Coalgebras provide effective models of data structures and state-transition systems. A virtual covariety is a class of coalgebras closed under coproducts, images of coalgebraic morphisms, and subcoalgebras defined by split equalisers. A covariety has the stronger property of closure under all subcoalgebras, and is behavioural if it is closed under domains of morphisms, or equivalently under images of bisimulations. There are many computationally interesting properties that define classes of these kinds. We identify conditions on the underlying category of a comonad G which ensure that there is an exact correspondence between (behavioural/virtual) covarieties of G-coalgebras and subcomonads of G defined by comonad morphisms to G with natural categorical properties. We also relate this analysis to notions of coequationally defined classes of coalgebras.}, address = {Berlin / Heidelberg}, author = {Clouston, Ranald and Goldblatt, Robert}, booktitle = {Theoretical Aspects of Computing – ICTAC 2005: Second International Colloquium, Hanoi, Vietnam, October 17-21, 2005. Proceedings}, citeulike-article-id = {565385}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/11560647_19}, doi = {10.1007/11560647_19}, editor = {Hung, Dang and Wirsing, Martin}, journal = {Theoretical Aspects of Computing – ICTAC 2005: Second International Colloquium, Hanoi, Vietnam, October 17-21, 2005. Proceedings}, keywords = {coalgebra, comonad, covariety}, pages = {288--302}, posted-at = {2006-03-27 12:13:24}, priority = {0}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Covarieties of Coalgebras: Comonads and Coequations}, url = {http://dx.doi.org/10.1007/11560647_19}, volume = {3722}, year = {2005} }

TY - CONF ID - citeulike:565385 L3 - citeulike-article-id:565385 N2 - Coalgebras provide effective models of data structures and state-transition systems. A virtual covariety is a class of coalgebras closed under coproducts, images of coalgebraic morphisms, and subcoalgebras defined by split equalisers. A covariety has the stronger property of closure under all subcoalgebras, and is behavioural if it is closed under domains of morphisms, or equivalently under images of bisimulations. There are many computationally interesting properties that define classes of these kinds. We identify conditions on the underlying category of a comonad G which ensure that there is an exact correspondence between (behavioural/virtual) covarieties of G-coalgebras and subcomonads of G defined by comonad morphisms to G with natural categorical properties. We also relate this analysis to notions of coequationally defined classes of coalgebras. JF - Theoretical Aspects of Computing – ICTAC 2005: Second International Colloquium, Hanoi, Vietnam, October 17-21, 2005. Proceedings SE - Lecture Notes in Computer Science AD - Berlin / Heidelberg EP - 302 TI - Covarieties of Coalgebras: Comonads and Coequations PB - Springer VL - 3722 T2 - Theoretical Aspects of Computing – ICTAC 2005: Second International Colloquium, Hanoi, Vietnam, October 17-21, 2005. Proceedings SP - 288 KW - coalgebra KW - comonad KW - covariety AU - Clouston, Ranald AU - Goldblatt, Robert A2 - Hung, Dang A2 - Wirsing, Martin PY - 2005/// UR - http://dx.doi.org/10.1007/11560647_19 ER -