Categorical Primitives for Agent Memory: A Foundational Proposal

We propose a categorical foundation for agent memory systems. Three categorical primitives are identified: Genesis (an operation category with initial object), Stratification (a Grothendieck opfibration encoding cross-layer type safety), and Relation Reification (a functor from the twisted arrow category lifting morphisms to first-class objects). The framework is developed in the tradition of categorical logic, with the opfibration formulation providing a structural account of type dependency across memory layers. The formal axiomatisation, soundness, completeness, and modular independence results are in the companion technical report [Mars 2026], DOI: 10.5281/zenodo.20279272. A mechanisation in a proof assistant via displayed categories (Ahrens-Lumsdaine 2019) is outlined as future work.

v1.2: converted to LaTeX/PDF (fixes math rendering); companion paper attribution clarified.