  This paper introduces the Categorical Graph Model for Conflict Resolution
(C-GMCR), a novel framework that integrates category theory into the
traditional Graph Model for Conflict Resolution (GMCR). The C-GMCR framework
provides a more abstract and general way to model and analyze conflict
resolution, enabling researchers to uncover deeper insights and connections. We
present the basic concepts, methods, and application of the C-GMCR framework to
the well-known Prisoner's Dilemma and other representative cases. The findings
suggest that the categorical approach offers new perspectives on stability
concepts and can potentially lead to the development of more effective conflict
resolution strategies.
