Completely integrable Hamiltonians defining classical mechanical systems of N coupled oscillators are obtained from Poisson realizations of Heisenberg–Weyl, harmonic oscillator and sl(2, IR) coalgebras. Various completely integrable deformations of such systems are constructed by considering quantum deformations of these algebras. Explicit expressions for all the deformed Hamiltonians and const...

In this paper we construct a coalgebra for an intrusion detection system to describe the behaviour of a packet stream together with selected actions in the case of intrusions. We start with an extension of the notion of the many-typed signature to the generalised signature and we construct the category of packets as a basic structure of our approach. A defined endofunctor captures the expected ...

The coalgebraic perspective on objects and classes in object-oriented programming is elaborated: objects consist of a (unique) identiier, a local state, and a collection of methods described as a coalgebra; classes are coalgebraic (behavioural) speciications of objects. The creation of a \new" object of a class is described in terms of the terminal coalgebra satisfying the speciication. We pres...

We generalize Stembridge's enriched P-partitions and use this theory to outline the structure of peak algebras for the symmetric group and the hyperoctahedral group. Whereas Stembridge's enriched P-partitions are related to quasisymmetric functions (the coalgebra dual to Solomon's type A descent algebra), our generalized enriched P-partitions are related to type B quasisymmetric functions (the ...

A coalgebra is introduced here as a model of a certain signature consisting of a type X with various \destructor" function symbols, satisfying certain equations. These destructor function symbols are like methods and attributes in object-oriented programming: they provide access to the type (or state) X. We show that the category of such coalgebras and structure preserving functions is comonadi...

An explicit formula for a strong connection form in a principal extension by a coseparable coalgebra is given. 1. In the studies of geometry of non-commutative principal bundles or coalgebraGalois extensions (cf. [7]) an important role is played by the notion of a strong connection (for the universal differential structure) first introduced in the context of Hopf-Galois extensions in [10]. The ...

We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for non-deterministic choice. In Set , this gives a category with ordinary transition systems as objects and with morphisms characterised in terms of a linear notion of bisimulation. The final object in this category is the canonical a...

We consider conditional transition systems, that allow to model software product lines with upgrades, in a coalgebraic setting. We show that, by using Birkhoff’s duality for distributive lattices, we obtain two equivalent Kleisli categories in which these coalgebras live: Kleisli categories based on the reader and on the so-called lattice monad over Poset. We study two different functors descri...

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. This is then put to use in the context of a Heyting pretopos with a class of small maps, in order to build the final coalgebra for the Ps functor. This is then prov...

The notion of locally finite part of the dual coalgebra of certain quantized coordinate rings is introduced. In the case of irreducible flag manifolds this locally finite part is shown to coincide with a natural quotient coalgebra U of Uq(g). On the way the coradical filtration of U is determined. A graded version of the duality between U and the quantized coordinate ring is established. This l...