  The operational semantics of interactive systems is usually described by
labeled transition systems. Abstract semantics (that is defined in terms of
bisimilarity) is characterized by the final morphism in some category of
coalgebras. Since the behaviour of interactive systems is for many reasons
infinite, symbolic semantics were introduced as a mean to define smaller,
possibly finite, transition systems, by employing symbolic actions and avoiding
some sources of infiniteness. Unfortunately, symbolic bisimilarity has a
different shape with respect to ordinary bisimilarity, and thus the standard
coalgebraic characterization does not work. In this paper, we introduce its
coalgebraic models. We will use as motivating examples two asynchronous
formalisms: open Petri nets and asynchronous pi-calculus. Indeed, as we have
shown in a previous paper, asynchronous bisimilarity can be seen as an instance
of symbolic bisimilarity.
