ALGEBRAIC CHARACTERIZATIONS FOR REDUCTION SYSTEMS
Anjeza Krakulli, Elton Pasku · Albanian Journal of Mathematics · 2012
We give algebraic characterizations for a reduction system to be respectively Noetherian and confluent, and for a Noetherian reduction system to be confluent. The characterization of a confluent reduction system (A,→) is based on a relationship between the confluence of the system and the exactness of the colimit functor colim : AbA→Ab where A is the small category with objects the elements of A and arrows a→b whenever b is a consequence of a in the system.