An abstract evolution system is a category endowed with a fixed family of arrows (called transitions) and with a distinguished object, called the origin. An evolution is an infinite sequence of transitions starting from the origin. We will show that evolution systems provide a good framework for the study of highly symmetric mathematical structures, namely those having rich automorphism groups. On the other hand, evolution systems also describe terminating transition systems, leading to an extension of the celebrated Newman's Lemma: A locally confluent terminating system is confluent.
(Joint work with P. Radecka)
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