Coalgebraic structures in module theory

Coalgebraic Correspondence Theory

We lay the foundations of a first-order correspondence theory for coalgebraic logics that makes the transition structure explicit in the first-order modelling. In particular, we prove a coalgebraic version of the van Benthem/Rosen theorem stating that both over arbitrary structures and over finite structures, coalgebraic modal logic is precisely the bisimulation invariant fragment of first-orde...

Combinatorial Models for Coalgebraic Structures

We introduce a convenient category of combinatorial objects, known as cell-sets, on which we study the properties of the appropriate free abelian group functor. We obtain a versatile generalization of the notion of incidence coalgebra, giving rise to an abundance of coalgebras, Hopf algebras, and comodules, all of whose structure constants are positive integers with respect to certain preferred...

Coalgebraic Representation Theory of Fractals

Coalgebraic Automata Theory: Basic Results

We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of the theory of coalgebra automata. In particular, we prove the following results for any functor F that preserves weak pullbacks. We show that the class of recognizable languages of F-coalgebras is closed under taking unions, intersections, and projections. We a...

A Coalgebraic Theory of Reactive Systems

In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, under rather restrictive conditions, the compositionality of the abstract semantics (bisimilarity). Universal Coalgebra provides a categorical framework where bisimilarity can be ch...