Extensional quotient coalgebras

On Simple and Extensional

The notions of simplicity and extensionality for coalgebras are generalized beyond Set and a study of the internal dynamics of extensional coalgebras yields the notion of unitary coalgebras. In some cases, unitary coalgebras include extensional ones. Under some reasonable circumstances, both notions of simplicity and extensionality agree. Other extensions of simplicity and extensionality are ∗−...

Stone coalgebras

In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor on the category of sets. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. T...

Topology on Coalgebras

Wellfounded coalgebras

For an endofunctor H an initial algebra I has, by Lambek’s Lemma, invertible structure map, thus, it can be considered as a coalgebra. We call an H-coalgebra wellfounded if it has a coalgebra homomorphism into I. This is equivalent to the wellfoundedness in Taylor’s “Practical Foundations”, defined by means of an induction principle. And it is also equivalent to the recursivity studied by Capre...

Steenrod coalgebras

Article history: Received 4 December 2013 Received in revised form 23 February 2015 Accepted 24 February 2015 Available online 5 March 2015