  In the simplest form of event structure, a prime event structure, an event is
associated with a unique causal history, its prime cause. However, it is quite
common for an event to have disjunctive causes in that it can be enabled by any
one of multiple sets of causes. Sometimes the sets of causes may be mutually
exclusive, inconsistent one with another, and sometimes not, in which case they
coexist consistently and constitute parallel causes of the event. The
established model of general event structures can model parallel causes. On
occasion however such a model abstracts too far away from the precise causal
histories of events to be directly useful. For example, sometimes one needs to
associate probabilities with different, possibly coexisting, causal histories
of a common event. Ideally, the causal histories of a general event structure
would correspond to the configurations of its causal unfolding to a prime event
structure; and the causal unfolding would arise as a right adjoint to the
embedding of prime in general event structures. But there is no such
adjunction. However, a slight extension of prime event structures remedies this
defect and provides a causal unfolding as a universal construction. Prime event
structures are extended with an equivalence relation in order to dissociate the
two roles, that of an event and its enabling; in effect, prime causes are
labelled by a disjunctive event, an equivalence class of its prime causes. With
this enrichment a suitable causal unfolding appears as a pseudo right adjoint.
The adjunction relies critically on the central and subtle notion of extremal
causal realisation as an embodiment of causal history. Finally, we explore
subcategories which support parallel causes as well the key operations needed
in developing probabilistic distributed strategies with parallel causes.
