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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Covarieties of Coalgebras: Comonads and Coequations
verfasst von : Ranald Clouston, Robert Goldblatt
Erschienen in: Theoretical Aspects of Computing – ICTAC 2005
Verlag: Springer Berlin Heidelberg
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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
$\mathbb{G}$
which ensure that there is an exact correspondence between (behavioural/virtual) covarieties of
$\mathbb{G}$
-coalgebras and
subcomonads
of
$\mathbb{G}$
defined by comonad morphisms to
$\mathbb{G}$
with natural categorical properties. We also relate this analysis to notions of
coequationally defined
classes of coalgebras.