We define families of posets, ordered by prefixes, as the counterpart of the usual families of configurations ordered by subsets. On these objects we define two types of morphism, event and order morphisms, resulting in categories FPos and FPosv. We then show the following: - Families of posets, in contrast to families of configurations, are always prime algebraic; in fact the category FPosv is equivalent to the category of prime algebraic domains. - On the level of events, FPos is equivalent to the category of prime algebraic domains with an additional relation encoding event identity. - The (abstract) event identity relation can be used to characterize concrete relations between events such as binary conflict and causal flow. - One can characterize a wide range of event-based models existing in the literature as families of posets satisfying certain specific structural conditions formulated in terms of event identity.