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

Categorical Approach to Conflict Resolution: Integrating Category Theory into the Graph Model for Conflict Resolution