Observational Ultrapowers of Polynomial Coalgebras

A Calculus of Terms for Coalgebras of Polynomial Functors

A syntax and semantics of types, terms and formulas for coalgebras of polynomial functors is developed, extending earlier work [4] on monomial coalgebras to include functors constructed using coproducts. A modified ultrapower construction for polynomial coalgebras is introduced, adapting the conventional ultrapower to retain only those states that evaluate observable terms in a standard way. A ...

A Kleene Theorem for Polynomial Coalgebras

For polynomial functors G, we show how to generalize the classical notion of regular expression to G-coalgebras. We introduce a language of expressions for describing elements of the final G-coalgebra and, analogously to Kleene’s theorem, we show the correspondence between expressions and finite G-coalgebras.

Coalgebras for Binary Methods: Properties of Bisimulations and Invariants

COALGEBRAS FOR BINARY METHODS: PROPERTIES OF BISIMULATIONS AND INVARIANTS HENDRIK TEWS 1 Abstract. Coalgebras for endofunctors C C can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors Cop C C . This extension allows t...

N ov 2 00 3 Symmetric Coalgebras

We construct a structure of a ring with local units on a co-Frobenius coalgebra. We study a special class of co-Frobenius coalgebras whose objects we call symmetric coalgebras. We prove that any semiperfect coalgebra can be embedded in a symmetric coalgebra. A dual version of Brauer's equivalence theorem is presented, allowing a characterization of symmetric coalgebras by comparing certain func...

Equational Logi of Polynomial Coalgebras