Formalizing Structural Semiotics: A Category-Theoretic Approach to Actantial Systems

In this article we present a categorical reconstruction of the actantial model introduced by A. J. Greimas in structural semiotics. Using Spivak and Kent’s framework of ontological logs and schema-based categories, the actantial system is formalized as a categorical schema whose Objects and morphisms encode relational roles in narrative structures. Standard categorical constructions such as pullbacks, morphism images, comma categories, and functors are used both to formalize the actantial relations identified by Greimas and to reveal additional structural relations that emerge from the categorical treatment of the model. By translating the actantial model into a schema equipped with instances, the framework provides a precise account of actantial roles, their compositional properties, and their realization in discourse. Functorial and profunctorial mappings are used to model the migration of narrative instances between schemas and the correspondence between abstract roles and textual fragments, offering a formal account of Greimas’s distinction between the narrative and discursive planes. Our approach adopts a relational, extensional perspective in which actantial roles are characterized by their participation in networks of relations and instances. The results illustrate how categorical schemas can function as a unifying formalism for role-based conceptual systems, with applications in comparative narrative analysis.