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Observational Ultraproducts of Polynomial Coalgebras
, 2002
"... Coalgebras of polynomial functors constructed from sets of observable elements have been found useful in modelling various kinds of data types and statetransition systems. ..."
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Cited by 6 (3 self)
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Coalgebras of polynomial functors constructed from sets of observable elements have been found useful in modelling various kinds of data types and statetransition systems.
Logics Admitting Final Semantics
 In Foundations of Software Science and Computation Structures, volume 2303 of LNCS
, 2002
"... A logic for coalgebras is said to admit final semantics iff up to some technical requirementsall definable classes contain a fully abstract final coalgebra. It is shown that a logic admits final semantics iff the formulas of the logic are preserved under coproducts (disjoint unions) and qu ..."
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A logic for coalgebras is said to admit final semantics iff up to some technical requirementsall definable classes contain a fully abstract final coalgebra. It is shown that a logic admits final semantics iff the formulas of the logic are preserved under coproducts (disjoint unions) and quotients (homomorphic images).
Under consideration for publication in Math. Struct. in Comp. Science A Comonadic Account of Behavioural
, 2002
"... A class K of coalgebras for an endofunctor T: Set → Set is a behavioural covariety if it is closed under disjoint unions and images of bisimulation relations (hence closed under images and domains of coalgebraic morphisms, including subcoalgebras). K may be thought of as the class of all coalgebras ..."
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A class K of coalgebras for an endofunctor T: Set → Set is a behavioural covariety if it is closed under disjoint unions and images of bisimulation relations (hence closed under images and domains of coalgebraic morphisms, including subcoalgebras). K may be thought of as the class of all coalgebras that satisfy some computationally significant property. In any logical system suitable for specifying properties of statetransition systems in the HennessyMilner style, each formula will define a class of models that is a behavioural covariety. Assume that the forgetful functor on Tcoalgebras has a right adjoint, providing for the construction of cofree coalgebras, and let G T be the comonad arising from this adjunction. Then we show that behavioural covarieties K are (isomorphic to) the EilenbergMoore categories of coalgebras for certain comonads G K naturally associated with G T. These are called pure subcomonads of G T, and a categorical characterization of them is given, involving a pullback condition on the naturality squares of a transformation from G K to G T. We show that there is a bijective correspondence between behavioural covarieties of Tcoalgebras and isomorphism classes of pure subcomonads of G T.