Working Paper: Towards a Category-theoretic Comparative Framework for Artificial General Intelligence

arXiv cs.AI / 4/1/2026

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Key Points

The paper argues that AGI lacks a single formal definition and that existing benchmarking frameworks are limited, motivating a new unified approach.
It proposes an algebraic, category-theoretic comparative framework to describe, analyze, and compare different AGI architectures such as RL, Universal AI, Active Inference, CRL, and schema-based learning.
As an initial exercise, it works through category-theoretic formulations involving RL, causal RL, and SBL, aiming to surface both commonalities and differences across these architectures.
The framework is intended to support formal definitions of architectural, informational, and semantic properties, along with empirical evaluation in environments with explicitly characterized features.
The authors position the work as a first step toward a broader research program integrating agent realization, agent–environment interaction, behavioral development over time, and evaluation under the same formal foundation.

Abstract

AGI has become the Holly Grail of AI with the promise of level intelligence and the major Tech companies around the world are investing unprecedented amounts of resources in its pursuit. Yet, there does not exist a single formal definition and only some empirical AGI benchmarking frameworks currently exist. The main purpose of this paper is to develop a general, algebraic and category theoretic framework for describing, comparing and analysing different possible AGI architectures. Thus, this Category theoretic formalization would also allow to compare different possible candidate AGI architectures, such as, RL, Universal AI, Active Inference, CRL, Schema based Learning, etc. It will allow to unambiguously expose their commonalities and differences, and what is even more important, expose areas for future research. From the applied Category theoretic point of view, we take as inspiration Machines in a Category to provide a modern view of AGI Architectures in a Category. More specifically, this first position paper provides, on one hand, a first exercise on RL, Causal RL and SBL Architectures in a Category, and on the other hand, it is a first step on a broader research program that seeks to provide a unified formal foundation for AGI systems, integrating architectural structure, informational organization, agent realization, agent and environment interaction, behavioural development over time, and the empirical evaluation of properties. This framework is also intended to support the definition of architectural properties, both syntactic and informational, as well as semantic properties of agents and their assessment in environments with explicitly characterized features. We claim that Category Theory and AGI will have a very symbiotic relation.