Relational properties of sequential composition of coalgebras

• Relation algebraic treatment of coalgebras and bisimulation.
• Definition of Sequential Composition of Coalgebras in arbitrary Dedekind categories.
• Basic Properties of this operation up to bisimulation.
• Solution to recursive equations based on sequential composition.

In this paper we define a sequential composition for arbitrary coalgebras in a Dedekind category. We show some basic algebraic properties of this operation up to bisimulation. Furthermore, we consider certain recursive equations and provide an explicit solution, i.e., a solution not based on an iterative process.