on descent for coalgebras and type transformations

On descent for coalgebras and type transformations

We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...

On Coalgebras and Type Transformations

We show that for an arbitrary Set-endofunctor T the generalized membership function given by a sub-cartesian transformation μ from T to the filter functor F can be alternatively defined by the collection of subcoalgebras of constant T -coalgebras. Sub-natural transformations ε between any two functors S and T are shown to be sub-cartesian if and only if they respect μ. The class of T -coalgebra...

Coalgebras Of Bounded Type

Using results of Trnková, we first show that subcoalgebras are always closed under finite intersections. Assuming that the type functor F is bounded, we obtain a concrete representation of the terminal F-coalgebra. Several equivalent characterizations of boundedness are provided.

Weak Bisimulation for Action-Type Coalgebras

We propose a coalgebraic definition of weak bisimulation for a class of coalgebras obtained from bifunctors in Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The transformation consists of two steps: First, the behaviour on actions is expanded to behaviour on finite words. Second, the behaviour on finite words is taken modulo the hiding of invisi...

Topology on Coalgebras

Coalgebras in functional programming and type theory

This is a survey article on the use of coalgebras in functional programming and type theory. It presents the basic theory underlying the implementation of coinductive types, families and predicates. It gives an overview of the application of corecursive methods to the study of general recursion, formal power series, tabulations of functions on inductive data. It also sketches some advanced topi...