Abstract
Relation lifting [Hermida, C. and B. Jacobs, Structural induction and coinduction in a fibrational setting, Information and Computation 145 (1998), pp. 107–152] extends an endofunctor F:C→C to a functor Rel(F):Rel(C)→Rel(C), where Rel(C) is a suitable category of relations over C. The relation lifting for the functor F can be used to define the notion of bisimulation for coalgebras X→F(X). The related notion of predicate lifting can be used to define invariants for F–coalgebras. Predicate and relation lifting can be directly defined for a rich class of polynomial functors [Hensel, U. and B. Jacobs, Proof principles for datatypes with iterated recursion, in: E. Moggi and G. Rosolini, editors, Category Theory and Computer Science, LNCS 1290 (1997), pp. 220–241; Hermida, C. and B. Jacobs, Structural induction and coinduction in a fibrational setting, Information and Computation 145 (1998), pp. 107–152; Tews, H., Coalgebras for binary methods: Properties of bisimulations and invariants, Theoretical informatics and applications 35 (2001), pp. 83–111]. In this paper I investigate the case where the functor F is defined as the initial semantics of a (single sorted) parametric algebraic specification.
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