We prove that iteration theories can be introduced as algebras for the monad Rat on the category of signatures assigning to every signature Σ the rational-Σ-tree signature. This supports the result… Expand

It is proved that whenever an endofunctor H of a category has final coalgebras for all functors H(-) + X, then those coalgeBRas, TX, form a monad, which is a free completely iterative monad on H.Expand

The monad given by free completely iterative algebras is proved to be the freecompletely iterative monad on the given endofunctor, which simplifies substantially all previous descriptions of these monads.Expand

This paper uses the coalgebraic view on systems to derive, in a uniform way, abstract procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization.Expand

For finitary set functors preserving inverse images, recursive coalgebras A of Paul Taylor are proved to be precisely those for which the system described by A always halts in finitely many steps.

This work introduces varieties of languages in a category C, and proves that they correspond to pseudovarieties of monoids in a closed monoidal category D, provided that C and D are dual on the level of finite objects.Expand

It is proved that the category of Elgot algebras is the Eilenberg–Moore category of the monad given by a free iterative theory, and two axioms stem canonically from Elgot’s iterative theories.Expand

A notion of graded algebras is introduced and it is shown how they play the role of formulas in trace logics and how they come with a notion of depth that corresponds, e.g., to trace length or bisimulation depth.Expand

This paper shows that by starting with ‘iterative algebras’, that is, algeBRas admitting a unique solution of all systems of flat recursive equations, a free iterative theory is obtained as the theory of free iteratives alge bras.Expand

This article investigates under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalized powerset construction that determinizes coalgebras.Expand