Kleisli semantics and hypergraph composition for Greimasian narrative programs

TL;DR

This paper introduces a category-theoretic framework for modeling Greimasian narrative programs, using Kleisli semantics and hypergraph composition to formalize their structure and dynamics.

Contribution

It develops a novel categorical formalization of narrative programs, integrating monads and hypergraph categories to capture their compositional and dynamic aspects.

Findings

Provides a formal semantics for actant configurations using List and Maybe monads.

Models narrative composition as wiring diagrams in a hypergraph category.

Connects data representations of narrative elements with their discourse realization.

Abstract

This article proposes a category-theoretic formalization of Greimasian narrative programs (NPs) that makes their compositional structure mathematically precise. Building on a reconstruction of the actantial model as a categorical schema, we introduce a refined typological schema of actants and derive Set-valued instances corresponding to role-indexed elements of a narrative. NPs are represented within a categorical schema whose morphisms are interpreted using monads on Set. In particular, the List monad provides a Kleisli semantics for modeling non-atomic, list-valued actantial configurations, while the Maybe monad encodes optional dependencies between programs. This yields a minimal representation of narrative programs as structured data with an intrinsic compositional interpretation. To account for the dynamics of narrative formation, we lift these constructions into a diagrammatic setting by freely generating a symmetric monoidal category, and subsequently a hypergraph category, from the set of actants. In this framework, narrative programs act as generators of morphisms, and their composition is realized through wiring diagrams. A narrative trajectory is thereby interpreted as a single composite morphism. This approach provides a unified mathematical framework for structural semiotics, connecting data-level representations of narrative elements with their compositional realization in discourse.