It is shown that quantum homogeneous spaces of a quantum group H can be viewed as fibres of quantum fibrations with the total space H that are dual to coalgebra bundles. As concrete examples of such structures the fibrations with the quantum 2-sphere and the quantum hyperboloid fibres are considered.

Accessible set functors can be presented by signatures and equations as quotients of polynomial functors. We determine how preservation of pullbacks and other related properties (often applied in coalgebra) are re ected in the structure of the system of equations.

We give a new, significantly shorter proof of the completeness of the left-handed star rule of Kleene algebra. The proof reveals the rich interaction of algebra and coalgebra in the theory.

We prove that any endofunctor on a class-theoretic category has a final coalgebra. Moreover, we characterize functors on set-theoretic categories which are identical on objects, and functors which are constant on objects.

The weak-* topology is seen to play an important role in the study of various finiteness conditions one may place on a coalgebra C and its dual algebra C*. Here we examine the interplay between the topology and the structure of ideals of 0*. The basic theory has been worked out for the commutative and almost connected cases (see [2]). Our basic tool for reducing to the almost connected case is ...

Entwined modules arose from the coalgebra-Galois theory. They are a generalisation of unified Doi-Hopf modules. In this paper, Frobenius properties and Maschke-type theorems, known for Doi-Hopf modules are extended to the case of entwined modules.

Universal Coalgebra provides the notion of a coalgebra as the natural mathematical generalization of state-based evolving systems such as (infinite) words, trees, and transition systems. We lift the theory of parity automata to a coalgebraic level of abstraction by introducing, for a set Λ of predicate liftings associated with a set functor T , the notion of a Λ-automata operating on coalgebras...

In this paper we address the issue of providing a structured coalgebra presentation of transition systems with algebraic structure on states determined by an equational specification Γ. More precisely, we aim at representing such systems as coalgebras for an endofunctor on the category of Γ-algebras. The systems we consider are specified by using a quite general format of SOS rules, the algebra...