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.

翻译：在事件结构的最简单形式——原始事件结构中，每个事件关联唯一因果历史，即其原始因。然而，事件具有析取因的情况相当普遍，即它可由多组原因中的任意一组所使能。这些原因组可能互斥且彼此不一致，也可能并非如此——此时它们一致共存并构成事件的并行因。已建立的通用事件结构模型能够建模并行因，但有时此类模型过度抽象，偏离了事件精确的因果历史，从而难以直接应用。例如，有时需要为同一事件的不同（可能共存）因果历史分配概率。理想情况下，通用事件结构的因果历史应与其展开为原始事件结构的因果展开之配置相对应，且该因果展开应作为原始事件结构嵌入通用事件结构的右伴随出现。然而，这样的伴随并不存在。不过，对原始事件结构的轻微扩展可弥补这一缺陷，并将因果展开视为一种普适构造。我们通过引入等价关系扩展原始事件结构，以分离事件及其使能的双重角色：实际上，原始因被标记为析取事件（即其原始因的等价类）。借助这一强化，适当的因果展开以伪右伴随的形式出现。该伴随关系关键依赖于“极值因果实现”这一核心而微妙的概念，作为因果历史的体现。最后，我们探索支撑并行因的子范畴，以及开发含并行因的概率化分布式策略所需的关键操作。