 
Summary: Discrete Mathematics and Theoretical Computer Science DMTCS vol. 8, 2006, 249272
A Cartesian Closed Category of Event
Structures with Quotients
Samy Abbes
LIAFA Universit´e Paris 7. France
received Feb 8, 2006, revised May 23, 2006, accepted Sep 3, 2006.
We introduce a new class of morphisms for event structures. The category obtained is cartesian closed, and a natural
notion of quotient event structure is defined within it. We study in particular the topological space of maximal con
figurations of quotient event structures. We introduce the compression of event structures as an example of quotient:
the compression of an event structure E is a minimal event structure with the same space of maximal configurations
as E.
Keywords: event structure, maximal elements, quotient semantics
1 Introduction
Prime event structureswe say event structures for short, always meaning prime event structureshave
been introduced by Winskel as a model of concurrent computational processes [14]. Applications of event
structures to concurrency theory are numerous, in particular to the theory of Petri nets and to trace theory
[11, 13, 12]. An event structure is defined as a triple (E, , #), where (E, ) is a poset whose elements
are called events, and # is a binary symmetric and irreflexive relation satisfying e1#e2 e3 e1#e3.
The order relation is called the causality relation, while the relation # is called the conflict relation. An
event structure Ewe identify event structures and sets of eventsis called finitary if E is a countable
