arxiv: 2603.28906 · v3 · submitted 2026-03-30 · 💻 cs.AI

Recognition: unknown

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

Pablo de los Riscos , Fernando J. Corbacho , Michael A. Arbib

Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:12 UTC · model grok-4.3

classification 💻 cs.AI

keywords category theoryartificial general intelligencecomparative frameworkreinforcement learningactive inferencecausal reinforcement learningschema-based learning

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The pith

Category theory supplies a formal algebraic language for describing and comparing AGI architectures such as reinforcement learning and active inference.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a category-theoretic framework to describe, compare, and analyze different AGI architectures in a unified way. Architectures including reinforcement learning, universal AI, active inference, causal reinforcement learning, and schema-based learning are modeled as objects and morphisms. This modeling is intended to expose their commonalities and differences unambiguously while identifying gaps for further work. The approach integrates architectural structure, informational organization, agent-environment interaction, behavioral development, and empirical evaluation. The authors conclude that category theory and AGI research will have a symbiotic relationship.

Core claim

By modeling AGI architectures as machines in a category, the framework provides a unified formal foundation that captures architectural structure, informational organization, agent realization, agent-environment interaction, behavioral development over time, and empirical evaluation of properties. This formalization allows unambiguous exposure of commonalities and differences across candidates such as RL, Universal AI, Active Inference, CRL, and Schema based Learning. It supports the definition of syntactic, informational, and semantic properties of agents and their assessment in environments with explicitly characterized features.

What carries the argument

Machines in a Category, which represents AGI architectures as objects with morphisms that encode transformations, interactions, or information flows.

Load-bearing premise

The essential behavioral and informational properties of existing AGI architectures can be captured faithfully by objects and morphisms in a category without significant loss.

What would settle it

A concrete attempt to embed the full structure of active inference, including free-energy minimization and belief updating, into a category reveals that key dynamic elements cannot be expressed using only the available objects and morphisms.

Figures

Figures reproduced from arXiv: 2603.28906 by Fernando J. Corbacho, Michael A. Arbib, Pablo de los Riscos.

**Figure 1.** Figure 1: Framework map 5.3.2 Practical verification workflow. Given a claim “agent F satisfies conclusion of theorem T” we require the following manifest: 1. the reference theorem T = (ΣT , Γ ⊢ φ) and, optionally, the trusted external proof π of T in the chosen logic; 2. a signature instantiation τ : ΣT → ΣA linking the theorem symbols to the semantic vocabulary of F, 3. evidence e witnessing MF |=ΣA τ (Γ); 4. the … view at source ↗

**Figure 2.** Figure 2: RL string diagram. 6.1.2 RL Knowledge layer The knowledge layer KnowRL is freely generated by the knowledge presentation KRL = (KT ypesRL, KGenRL, KEqRL, where: 21 [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗

**Figure 3.** Figure 3: CRL string diagram. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_3.png] view at source ↗

**Figure 4.** Figure 4: Figures of consecutive change steps over the CRL architecture. The changes done in each step compared with [PITH_FULL_IMAGE:figures/full_fig_p033_4.png] view at source ↗

**Figure 5.** Figure 5: SBL string diagram 6.4.2 SBL Knowledge level. The knowledge architecture KnowSBL is freely generated by the knowledge presentation KSBL = (KT ypesSBL, KGenSBL, KEqSBL) where: • KT ypesSBL = {ΣP erceptual, ΣMotor, ΣP redictive, ΣReward, ΣAbstract, {Θk},Mk}. The knowledge architecture KnowSBL comprises a heterogeneous family of schemas together with a global memory Mk and a global carrier of schemas {Θk}. • … view at source ↗

**Figure 6.** Figure 6: AIXI string diagram • KT ypesAIXI = {M, K, {E}, W}, were M is the knowledge unit representing the memory storing the history of the agent, K is the knowledge unit representing the universal kernel, {E} is the set of hypothesis about the potential next environments and W is the unit of knowledge that represent the beliefs, that is, the weights over the possible set of environments. • KGenAIXI is composed by… view at source ↗

**Figure 7.** Figure 7: Theoretical AIXI Workflow knowledge and implementation of each operator [PITH_FULL_IMAGE:figures/full_fig_p040_7.png] view at source ↗

**Figure 8.** Figure 8: Example paths in the topological space of [PITH_FULL_IMAGE:figures/full_fig_p047_8.png] view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a position paper sketching a category-theoretic research program for comparing AGI architectures like RL and Active Inference, but it stops at high-level outlines without any completed formal constructions.

read the letter

The main thing to know is that this paper proposes using category theory to give a shared language for comparing AGI candidates such as reinforcement learning, causal RL, active inference, and schema-based learning, but it does not yet deliver the actual categories, functors, or comparisons it envisions. It draws inspiration from machines in a category and argues this approach could expose commonalities, differences, and open research areas more clearly than current empirical benchmarks allow. The motivation is reasonable: AGI still lacks a single formal definition, and algebraic tools might help organize the architectural and informational aspects across systems. The authors also sketch a wider program that would cover agent-environment interaction, behavioral development, and property evaluation in characterized environments. That framing is coherent and points to a plausible long-term direction. The limitation is that the work remains prospective. The text describes initial exercises for placing RL, causal RL, and schema-based learning into a categorical setting, yet it supplies no explicit objects, morphisms, functors, or preservation results that could be checked or built upon. Claims about unambiguous exposure of commonalities stay at the level of future promise rather than demonstrated outcomes. No derivations or concrete examples appear in the available sections. This paper is mainly for researchers already working on formal methods in AI or cognitive modeling who want to see how category theory might be extended to AGI. A reader seeking new theorems, reproducible comparisons, or immediate practical tools will not find them here. It deserves peer review because the proposal is internally consistent, engages with relevant prior work on category theory in AI, and could benefit from referee feedback on how to turn the sketches into usable formal content.

Referee Report

2 major / 2 minor

Summary. The manuscript is a position paper proposing a category-theoretic framework, inspired by machines in a category, for describing, comparing, and analyzing AGI architectures such as RL, Universal AI, Active Inference, CRL, and Schema-based Learning. It includes initial high-level exercises for placing RL, Causal RL, and Schema-based Learning into a categorical setting and outlines a broader research program integrating architectural structure, informational organization, agent-environment interaction, behavioral development, and empirical evaluation. The central claim is that this approach will expose commonalities and differences unambiguously and establish a symbiotic relation between category theory and AGI.

Significance. If fully developed with concrete categorical representations, functors, and comparison results, the framework could provide a valuable unified formal language for AGI research, enabling precise identification of architectural gaps and guiding hybrid designs. As presented, however, its significance remains prospective and limited to sketching a research direction without completed formalisms or validations.

major comments (2)

[Initial exercises on RL, Causal RL, and SBL] The initial exercises for RL, Causal RL, and SBL are described only at a conceptual level without specifying the underlying category, objects, morphisms, or any functors/natural transformations. This leaves the claim that such representations can faithfully capture essential behavioral and informational properties without loss unsupported and unevaluable.
[Broader research program outline] The assertion that the framework will support definitions of syntactic, informational, and semantic properties, as well as their assessment in characterized environments, is stated without any preliminary definitions, examples, or preservation theorems, rendering the broader research program claim load-bearing but unsubstantiated.

minor comments (2)

[Abstract] Typo in abstract: 'Holly Grail' should read 'Holy Grail'.
[Throughout] The manuscript would benefit from citing prior categorical approaches to AI, reinforcement learning, and active inference to better contextualize the proposal.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our position paper. We address the major comments point by point below, clarifying the intended scope while committing to targeted improvements.

read point-by-point responses

Referee: [Initial exercises on RL, Causal RL, and SBL] The initial exercises for RL, Causal RL, and SBL are described only at a conceptual level without specifying the underlying category, objects, morphisms, or any functors/natural transformations. This leaves the claim that such representations can faithfully capture essential behavioral and informational properties without loss unsupported and unevaluable.

Authors: We agree that the exercises remain at a conceptual level in the current draft. As the manuscript is explicitly framed as a position paper providing 'initial exercises' and 'a first step,' the intent was to outline the approach rather than deliver complete formalisms. To strengthen evaluability, we will revise the section to identify the underlying categories (e.g., a category of agents with morphisms as behavior-preserving maps), specify key objects and morphisms for each architecture, and introduce at least one functor relating RL and Causal RL. This will illustrate the capture of properties more concretely while preserving the paper's prospective character. revision: partial
Referee: [Broader research program outline] The assertion that the framework will support definitions of syntactic, informational, and semantic properties, as well as their assessment in characterized environments, is stated without any preliminary definitions, examples, or preservation theorems, rendering the broader research program claim load-bearing but unsubstantiated.

Authors: The manuscript presents these capabilities as part of a longer-term research program rather than fully realized results. We acknowledge that preliminary content would better support the claims. In revision, we will add a concise example subsection defining one syntactic property (e.g., functorial preservation of composability) with a simple preservation statement under a functor to a category of environments, plus an illustration of assessment in a characterized setting. This will ground the outline without expanding beyond the position-paper scope. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The manuscript is a position paper that proposes a high-level category-theoretic framework for comparing AGI architectures without presenting any derivations, equations, fitted parameters, or completed theorems. All content consists of prospective outlines and initial exercises for representing RL, Causal RL, and Schema-based Learning in categorical terms, with no load-bearing steps that reduce by construction to self-definitions or self-citations. The central claim remains prospective and does not rely on any internal reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The proposal rests on standard category theory (objects, morphisms, functors) treated as background mathematics. No free parameters are introduced. No new entities are postulated.

axioms (1)

standard math Standard axioms of category theory (composition, identities, associativity)
Invoked implicitly when modeling architectures as categories.

pith-pipeline@v0.9.0 · 5585 in / 1128 out tokens · 30110 ms · 2026-05-14T21:12:27.280525+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Harness Engineering as Categorical Architecture
cs.PL 2026-05 unverdicted novelty 5.0

Categorical Architecture triple (G, Know, Phi) supplies the formal theory for composing LLM agent harnesses with structurally preserved certificates.

Reference graph

Works this paper leans on

97 extracted references · 97 canonical work pages · cited by 1 Pith paper · 1 internal anchor

[1]

Artificial General Intelligence: Concept, State of the Art, and Future Prospects

Ben Goertzel. Artificial General Intelligence: Concept, State of the Art, and Future Prospects. Journal of Artificial General Intelligence, 5(1):1–48, December 2014

work page 2014
[2]

Bridging agi theory and practice with galois connections

Ben Goertzel. Bridging agi theory and practice with galois connections. In Patrick Hammer, Marjan Alirezaie, and Claes Strannegård, editors,Artificial General Intelligence, pages 115–125, Cham, 2023. Springer Nature Switzerland

work page 2023
[3]

Engineering General Intelligence, Part 1: A Path to Advanced AGI via Embodied Learning and Cognitive Synergy, volume 5 ofAtlantis Thinking Machines

Ben Goertzel, Cassio Pennachin, and Nil Geisweiller. Engineering General Intelligence, Part 1: A Path to Advanced AGI via Embodied Learning and Cognitive Synergy, volume 5 ofAtlantis Thinking Machines. Atlantis Press, Amsterdam, Paris, Beijing, 2014

work page 2014
[4]

Engineering General Intelligence, Part 2: The CogPrime Architecture for Integrative, Embodied AGI, volume 6 ofAtlantis Thinking Machines

Ben Goertzel, Cassio Pennachin, and Nil Geisweiller. Engineering General Intelligence, Part 2: The CogPrime Architecture for Integrative, Embodied AGI, volume 6 ofAtlantis Thinking Machines. Atlantis Press, Paris; Amsterdam, 2014

work page 2014
[5]

Cognitive robotics using the soar cognitive architecture.AAAI Workshop - Technical Report, 01 2012

John Laird, Keegan Kinkade, Shiwali Mohan, and Joseph Xu. Cognitive robotics using the soar cognitive architecture.AAAI Workshop - Technical Report, 01 2012

work page 2012
[6]

A standard model of the mind: Toward a common computational framework across artificial intelligence, cognitive science, neuroscience, and robotics.AI Magazine, 38:13, 12 2017

John Laird, Christian Lebiere, and Paul Rosenbloom. A standard model of the mind: Toward a common computational framework across artificial intelligence, cognitive science, neuroscience, and robotics.AI Magazine, 38:13, 12 2017

work page 2017
[7]

Laird.The Soar Cognitive Architecture

John E. Laird.The Soar Cognitive Architecture. The MIT Press, Cambridge, MA, 2012. A Bradford Book

work page 2012
[8]

Laird and Paul S

John E. Laird and Paul S. Rosenbloom. Integrating execution, planning, and learning in soar for external environments. InProceedings of the Eighth National Conference on Artificial Intelligence - Volume 2, AAAI’90, page 1022–1029. AAAI Press, 1990

work page 1990
[9]

The sigma cognitive architecture and system: Towards functionally elegant grand unification

Paul Rosenbloom, Abram Demski, and V olkan Ustun. The sigma cognitive architecture and system: Towards functionally elegant grand unification. Journal of Artificial General Intelligence, 7, 01 2016

work page 2016
[10]

Rosenbloom, Abram Demski, and V olkan Ustun

Paul S. Rosenbloom, Abram Demski, and V olkan Ustun. Rethinking sigma’s graphical architecture: An extension to neural networks. In Bas Steunebrink, Pei Wang, and Ben Goertzel, editors,Proceedings of the Ninth Conference on Artificial General Intelligence, volume 9782 ofLecture Notes in Computer Science, pages 84–94, Berlin, 2016. Springer

work page 2016
[11]

Cambridge University Press, 2005

Ron Sun.The CLARION Cognitive Architecture: Extending Cognitive Modeling to Social Simulation. Cambridge University Press, 2005

work page 2005
[12]

Oxford Series on Cognitive Models and Architectures

Ron Sun.Anatomy of the Mind: Exploring Psychological Mechanisms and Processes with the Clarion Cognitive Architecture. Oxford Series on Cognitive Models and Architectures. Oxford University Press, Oxford, UK, 2016

work page 2016
[13]

Self-predictive universal ai

Elliot Catt, Jordi Grau-Moya, Marcus Hutter, Matthew Aitchison, Tim Genewein, Grégoire Delétang, Kevin Li, and Joel Veness. Self-predictive universal ai. In A. Oh, T. Naumann, A. Globerson, K. Saenko, M. Hardt, and S. Levine, editors, Advances in Neural Information Processing Systems, volume 36, pages 27181–27198. Curran Associates, Inc., 2023

work page 2023
[14]

A mathematical formulation of agi in the (c, u, v) framework

Di He, Cong Fang, Yisen Wang, Yujia Peng, Yizhou Wang, and Song-Chun Zhu. A mathematical formulation of agi in the (c, u, v) framework. Engineering, 2025

work page 2025
[15]

Texts in Theoretical Computer Science

Marcus Hutter.Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Germany, 2005

work page 2005
[16]

Chapman and Hall/CRC, New York, 1st edition, 2024

Marcus Hutter, David Quarel, and Elliot Catt.An Introduction to Universal Artificial Intelligence. Chapman and Hall/CRC, New York, 1st edition, 2024

work page 2024
[17]

Joel Veness, Kee Siong Ng, Marcus Hutter, William Uther, and D. Silver. A monte-carlo aixi approximation.Journal of Artificial Intelligence Research, 40:95–142, 01 2011

work page 2011
[18]

Springer Science & Business Media, 2012

Pei Wang and Ben Goertzel, editors.Theoretical Foundations of Artificial General Intelligence, volume 4 ofAtlantis Thinking Machines. Springer Science & Business Media, 2012

work page 2012
[19]

On the measure of intelligence, 2019

François Chollet. On the measure of intelligence, 2019

work page 2019
[20]

On defining artificial intelligence.Journal of Artificial General Intelligence, 10:1–37, 08 2019

Pei Wang. On defining artificial intelligence.Journal of Artificial General Intelligence, 10:1–37, 08 2019

work page 2019
[21]

A collection of definitions of intelligence.Advances in Artificial General Intelligence: Concepts, Architectures and Algorithms, 157, 07 2007

Shane Legg and Marcus Hutter. A collection of definitions of intelligence.Advances in Artificial General Intelligence: Concepts, Architectures and Algorithms, 157, 07 2007

work page 2007
[22]

Thórisson, Jordi Bieger, Xiang Li, and Pei Wang

Kristinn R. Thórisson, Jordi Bieger, Xiang Li, and Pei Wang. Cumulative learning. InArtificial General Intelligence, 12th International Conference, AGI 2019, volume 11654 ofLecture Notes in Computer Science, pages 198–208, Shenzhen, China, 2019. Springer

work page 2019
[23]

Pablo Riscos, Fernando Corbacho, and Michael A. Arbib. Working paper: Towards a category- theoretic comparative framework for artificial general intelligence, 2026

work page 2026
[24]

Fuzzy machines in a category.Bulletin of the Australian Mathematical Society, 13:169 – 210, 10 1975

Michael Arbib and Ernest Manes. Fuzzy machines in a category.Bulletin of the Australian Mathematical Society, 13:169 – 210, 10 1975

work page 1975
[25]

Arbib and Ernest G

Michael A. Arbib and Ernest G. Manes. Machines in a category: An expository introduction.SIAM Review, 16(2):163–192, 1974

work page 1974
[26]

Arbib and Ernest G

Michael A. Arbib and Ernest G. Manes. Adjoint machines, state-behavior machines, and duality. 49 Working paper: Towards a Category-theoretic Comparative Framework for AGI Journal of Pure and Applied Algebra, 6(3):313–344, 1975

work page 1975
[27]

Arbib and Ernest G

Michael A. Arbib and Ernest G. Manes. Machines in a category.Journal of Pure and Applied Algebra, 19:9–20, 1980

work page 1980
[28]

Araújo, and Petar Veliˇckovi´c

Bruno Gavranovi´c, Paul Lessard, Andrew Dudzik, Tamara V on Glehn, João G.M. Araújo, and Petar Veliˇckovi´c. Position: categorical deep learning is an algebraic theory of all architectures. InProceedings of the 41st International Conference on Machine Learning, ICML’24. JMLR.org, 2024

work page 2024
[29]

Category-theoretical and topos-theoretical frameworks in machine learning: A survey.Axioms, 14(3), 2025

Yiyang Jia, Guohong Peng, Zheng Yang, and Tianhao Chen. Category-theoretical and topos-theoretical frameworks in machine learning: A survey.Axioms, 14(3), 2025

work page 2025
[30]

Shiebler, B

D. Shiebler, B. Gavranovi´c, and P. Wilson. Category theory in machine learning.arxiv, 2021

work page 2021
[31]

Spivak, and Rémy Tuyéras

Brendan Fong, David I. Spivak, and Rémy Tuyéras. Backprop as functor: A compositional perspective on supervised learning.2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1–13, 2019

work page 2019
[32]

Value iteration is optic composition

Jules Hedges and Riu Rodríguez-Sakamoto. Value iteration is optic composition. InProceedings of Applied Category Theory 2022, Electronic Proceedings in Theoretical Computer Science, volume 380, page 417–432, 2023

work page 2022
[33]

Reinforcement learning in categorical cybernetics

Jules Hedges and Riu Rodríguez-Sakamoto. Reinforcement learning in categorical cybernetics. InProceedings of Applied Category Theory 2024, Electronic Proceedings in Theoretical Computer Science, volume 429, pages 270, 236, 2025

work page 2024
[34]

Categorical semantics of compositional reinforcement learning.Journal of Machine Learning Research, 26:1–37, 2025

Georgios Bakirtzis, Michail Savvas, and Ufuk Topcu. Categorical semantics of compositional reinforcement learning.Journal of Machine Learning Research, 26:1–37, 2025

work page 2025
[35]

Reduce, reuse, recycle: Categories for compositional reinforcement learning.European Conference in Artificial Intelligence ECAI-26, 2025

Georgios Bakirtzis, Michail Savvas, Ruihan Zhao, Sandeep Chinchali, and Ufuk Topcu. Reduce, reuse, recycle: Categories for compositional reinforcement learning.European Conference in Artificial Intelligence ECAI-26, 2025

work page 2025
[36]

Universal decision models

Sridhar Mahadevan. Universal decision models. CoRR, abs/2110.15431, 2021

work page arXiv 2021
[37]

Universal reinforcement learning in coalgebras: Asynchronous stochastic computation via conduction.CoRR, abs/2508.15128, 2025

Sridhar Mahadevan. Universal reinforcement learning in coalgebras: Asynchronous stochastic computation via conduction.CoRR, abs/2508.15128, 2025

work page arXiv 2025
[38]

Steunebrink.The Road to General Intelligence, 2, volume 1049 of Studies in Computational Intelligence

Jerry Swan, Eric Nivel, Neel Kant, Jules Hedges, Timothy Atkinson, and Bas R. Steunebrink.The Road to General Intelligence, 2, volume 1049 of Studies in Computational Intelligence. Springer, 2022

work page 2022
[39]

Towards foundations of categorical cybernetics

Mateo Capucci, Bruno Gavranovi´c, Jules Hedges, and Eigil Fjeldgren Rischel. Towards foundations of categorical cybernetics. in proceedings of applied category theory 2021 (act 2021). volume 372, pages 235––248., 2022

work page 2021
[40]

Category theory for artificial general intelligence

Vincent Abbott, Tom Xu, and Yoshihiro Maruyama. Category theory for artificial general intelligence. In Kristinn R. Thórisson, Peter Isaev, and Arash Sheikhlar, editors,Artificial General Intelligence - 17th International Conference, AGI 2024, Seattle, WA, USA, August 13-16, 2024, Proceedings, Lecture Notes in Computer Science, pages 119–129. Springer, 2024

work page 2024
[41]

Rethinking AI: from functions to functors

Sridhar Mahadevan. Rethinking AI: from functions to functors. In Sven Koenig, Chad Jenkins, and Matthew E. Taylor, editors,Fortieth AAAI Conference on Artificial Intelligence, Thirty-Eighth Conference on Innovative Applications of Artificial Intelligence, Sixteenth Symposium on Educational Advances in Artificial Intelligence, AAAI 2026, Singapore, January...

work page 2026
[42]

Computing with categories in machine learning, 2023

Eli Sennesh, Tom Xu, and Yoshihiro Maruyama. Computing with categories in machine learning, 2023

work page 2023
[43]

AGI from the perspectives of categorical logic and algebraic geometry

King-Yin Yan. AGI from the perspectives of categorical logic and algebraic geometry. In Kristinn R. Thórisson, Peter Isaev, and Arash Sheikhlar, editors,Artificial General Intelligence - 17th International Conference, AGI 2024, Seattle, WA, USA, August 13-16, 2024, Proceedings, Lecture Notes in Computer Science, pages 210–217. Springer, 2024

work page 2024
[44]

A categorical framework of general intelligence.CoRR, abs/2303.04571, 2023

Yang Yuan. A categorical framework of general intelligence.CoRR, abs/2303.04571, 2023

work page arXiv 2023
[45]

Baez and Jason Erbele

John C. Baez and Jason Erbele. Categories in control, 2015

work page 2015
[46]

Diagrammatic algebra: from linear to concurrent systems

Filippo Bonchi, Joshua Holland, Robin Piedeleu, Pawel Sobocinski, and Fabio Zanasi. Diagrammatic algebra: from linear to concurrent systems. Proceedings of the ACM on Programming Languages, 3:1 – 28, 2019

work page 2019
[47]

Spekkens

Bob Coecke, Tobias Fritz, and Robert W. Spekkens. A mathematical theory of resources.Information and Computation, 250:59–86, 2016. Quantum Physics and Logic

work page 2016
[48]

A categorical approach to open and interconnected dynamical systems

Brendan Fong, Paweł Soboci ´nski, and Paolo Rapisarda. A categorical approach to open and interconnected dynamical systems. In2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1–10, 2016

work page 2016
[49]

Towards a double operadic theory of systems.arXiv preprint arXiv:2505.18329, 2025

Sophie Libkind and David Jaz Myers. Towards a double operadic theory of systems.arXiv preprint arXiv:2505.18329, 2025

work page arXiv 2025
[50]

Double categories of open dynamical systems (extended abstract).Electronic Proceedings in Theoretical Computer Science, 333:154–167, February 2021

David Jaz Myers. Double categories of open dynamical systems (extended abstract).Electronic Proceedings in Theoretical Computer Science, 333:154–167, February 2021. 50 Working paper: Towards a Category-theoretic Comparative Framework for AGI

work page 2021
[51]

Categorical systems theory

David Jaz Myers. Categorical systems theory. Draft manuscript, 2023

work page 2023
[52]

Baez, Brendan Fong, and Blake S

John C. Baez, Brendan Fong, and Blake S. Pollard. A compositional framework for markov processes. Journal of Mathematical Physics, 57(3), March 2016

work page 2016
[53]

Evidential decision theory via partial markov categories

Elena Di Lavore and Mario Román. Evidential decision theory via partial markov categories. In 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1–14, 2023

work page 2023
[54]

Partial markov categories.CoRR, abs/2502.03477, 2025

Elena Di Lavore, Mario Román, and Paweł Soboci´nski. Partial markov categories.CoRR, abs/2502.03477, 2025

work page arXiv 2025
[55]

A synthetic approach to markov kernels, conditional independence and theorems on sufficient statistics.Advances in Mathematics, 370:107239, 2020

Tobias Fritz. A synthetic approach to markov kernels, conditional independence and theorems on sufficient statistics.Advances in Mathematics, 370:107239, 2020

work page 2020
[56]

Causal inference by string diagram surgery, 2019

Bart Jacobs, Aleks Kissinger, and Fabio Zanasi. Causal inference by string diagram surgery, 2019

work page 2019
[57]

A categorical semantics for causal structure

Aleks Kissinger and Sander Uijlen. A categorical semantics for causal structure. In2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1–12, 2017

work page 2017
[58]

Universal causality.Entropy, 25(4):574, 2023

Sridhar Mahadevan. Universal causality.Entropy, 25(4):574, 2023

work page 2023
[59]

Higher algebraic k-theory of causality.Entropy, 27(5), 2025

Sridhar Mahadevan. Higher algebraic k-theory of causality.Entropy, 27(5), 2025

work page 2025
[60]

Markov categories and entropy.IEEE Transactions on Information Theory, 70(3):1671– 1692, 2024

Paolo Perrone. Markov categories and entropy.IEEE Transactions on Information Theory, 70(3):1671– 1692, 2024

work page 2024
[61]

Pablo Riscos, Fernando Corbacho, and Michael A. Arbib. Working paper: Towards schema-based learning from a category-theoretic perspective, 2026

work page 2026
[62]

The algebra of open and interconnected systems, 2016

Brendan Fong. The algebra of open and interconnected systems, 2016

work page 2016
[63]

Brendan Fong and David I. Spivak. Hypergraph categories.Journal of Pure and Applied Algebra, 223(11):4746–4777, 2019

work page 2019
[64]

Rewriting in free hypergraph categories.Electronic Proceedings in Theoretical Computer Science, 263:16–30, December 2017

Fabio Zanasi. Rewriting in free hypergraph categories.Electronic Proceedings in Theoretical Computer Science, 263:16–30, December 2017

work page 2017
[65]

Seven sketches in compositionality: An invitation to applied category theory, 2018

Brendan Fong and David I Spivak. Seven sketches in compositionality: An invitation to applied category theory, 2018

work page 2018
[66]

A categorical manifesto

Joseph Goguen. A categorical manifesto. Mathematical Structures in Computer Science, 1, 12 2002

work page 2002
[67]

A category theory principle for cognitive science: Cognition as universal construction.Cognitive Studies: Bulletin of the Japanese Cognitive Science Society, pages 1–14, 2021

Steven Phillips. A category theory principle for cognitive science: Cognition as universal construction.Cognitive Studies: Bulletin of the Japanese Cognitive Science Society, pages 1–14, 2021

work page 2021
[68]

Michael A. Arbib. A common framework for automata theory and control theory.Journal of the Society for Industrial and Applied Mathematics Series A Control, 3(2):206–222, 1965

work page 1965
[69]

Michael A. Arbib. Schema theory. In Michael A. Arbib, editor,The Handbook of Brain Theory and Neural Networks. 2nd Edition, pages 993–999. MIT Press, 2002

work page 2002
[70]

A general (category theory) principle for general intelligence: Duality (adjointness)

Steven Phillips. A general (category theory) principle for general intelligence: Duality (adjointness). In Tom Everitt, Ben Goertzel, and Alexey Potapov, editors,Artificial General Intelligence - 10th International Conference, AGI 2017, Melbourne, VIC, Australia, August 15-18, 2017, Proceedings, Lecture Notes in Computer Science, pages 57–66. Springer, 2017

work page 2017
[71]

Spivak, and Eugene Lerman

David Vagner, David I. Spivak, and Eugene Lerman. Algebras of open dynamical systems on the operad of wiring diagrams.Theory and Applications of Categories, 30(51):1793–1822, 2015

work page 2015
[72]

Arbib and Ernest G

Michael A. Arbib and Ernest G. Manes. Arrows, structures, and functors: The categorical imperative. Academic Press, 1975

work page 1975
[73]

Springer, New York, 1998

Saunders Mac Lane.Categories for the Working Mathematician. Springer, New York, 1998. 2nd ed., Graduate Texts in Mathematics 5

work page 1998
[74]

David I. Spivak. Category theory for scientists (old version), 2013

work page 2013
[75]

J.A. Goguen. Discrete-time machines in closed monoidal categories. i.Journal of Computer and System Sciences, 10(1):1–43, 1975

work page 1975
[76]

Cambridge University Press, 2023

Ralf Hinze and Dan Marsden.Introducing String Diagrams: The Art of Category Theory. Cambridge University Press, 2023

work page 2023
[77]

J. A. Goguen. Minimal realization of machines in closed categories.Bulletin of the American Mathematical Society, 78(5):777 – 783, 1972

work page 1972
[78]

Sabadini

Piergiulio Katis and N. Sabadini. On the algebra of feedback and systems with boundary. 02 2000

work page 2000
[79]

Steven Phillips and William H. Wilson. Systematicity and a categorical theory of cognitive architecture: Universal construction in context.Frontiers in Psychology, V olume 7 - 2016, 2016

work page 2016
[80]

Jan C. Willems. The behavioral approach to open and interconnected systems.IEEE Control Systems Magazine, 27(6):46–99, 2007

work page 2007

Showing first 80 references.