Book 01 · The broad foundation

Categories for AGI

478 pagesDraftAugust 27, 2026
Cover of Categories for AGI by Sridhar Mahadevan

Scope

A detailed introduction to the application of category theory to formulate a research program in artificial general intelligence.

Start here

Begin here if category theory is new, or if you want the widest map of the research program before following a specialized path.

Chapter outline

Part I

A Categorical Language

p. 21
  1. Category Theory for AGIp. 23
  2. Functors for AGIp. 31
  3. Representable Functors and the Yoneda Lemmap. 43
  4. Diagrams and Universal Constructionsp. 49
Part II

Compositional Learning

p. 57
  1. Categorical Deep Learningp. 59
  2. Diagrammatic Backpropagationp. 69
Part III

Geometric and Kan Extension Transformers

p. 77
  1. Geometric Transformersp. 79
  2. Dynamic Compositionalityp. 95
  3. Information Regimes in Geometric Transformersp. 127
  4. Kan Extension and Topological Coend Transformersp. 137
  5. Structured Language Modelingp. 177
  6. Manifold Learning with Geometric Transformersp. 183
  7. Mean-Field Theory of Geometric Transformersp. 191
  8. Depth Sweeps for Geometric Transformersp. 199
Part IV

Categorical Models of Causality

p. 205
  1. Adjoint Functorsp. 207
  2. Causal Claims from Languagep. 213
  3. Temporal Diffusion over Causal Trajectoriesp. 221
  4. Building Agentic Systems using Kan Extension Transformersp. 243
  5. Topos Causal Modelsp. 257
  6. Judo Calculusp. 269
  7. Csql: Mapping Documents into Topos Causal Model Databasesp. 305
  8. Homotopy in Language and Causal Inferencep. 343
  9. Model Categories for Causality and Languagep. 357
  10. Predictive State Representations in a Toposp. 365
  11. Causal Density Functionsp. 397
Part V

Universal Decision Models

p. 407
  1. Universal Decisions with Kan Extensionsp. 409
  2. Universal Reinforcement Learningp. 423
  3. Deep URL with Geometric Transformersp. 427
Part VI

Frontiers of AGI

p. 435
  1. Consciousnessp. 437
  2. Universal Imitation Gamesp. 441
  3. Formal Verification Mapp. 445
  4. CLIFF Companionp. 451
  5. Code Companionp. 459

How to read the claims

This is a broad research-program book. Its exploratory chapters should be read as invitations and formal proposals, not as equally mature empirical systems.

Selected supporting record

Papers, software, and evidence packets

This is a claim-scoped selection, not a complete bibliography. Local experiment packets are described but not publicly attached.

Open the curated evidence library

Experiment-to-code map

From chapter summaries to executable records

Each family records its chapter destination, code package, executable entry points, result artifacts, and evidentiary boundary.

Open the complete experiment atlas

Code companions

Public repositories and release gaps

Public links open the inspectable GitHub package. A local-only package is shown explicitly so an unpublished research archive is never mistaken for a reproducible public release.

research archive

Geometric and Kan Extension Transformer archive

Working scripts and result directories for DB, GT, KET, language modeling, manifold, mean-field, and scaling studies. A curated public packet remains to be extracted.

Local only · curation required

research archive

BASKET and ROCKET experiment archive ↗

Public source-first BASKET and ROCKET workspace; large generated outputs remain outside the public repository and are represented separately as evidence records.

not specified

research archive

Kan-do DCDI experiment archive

Additional Judo Calculus drivers, regime-stability studies, and archived result tables used alongside Causal Discovery on Sheaves. A curated public packet remains to be prepared.

Local only · curation required

research archive

ATLAS CSQL database archive

Checked categorical SQL database instances and summaries used by the CSQL chapter.

Local only · curation required

research archive

GT RL Coalgebra archive

Thirty-run Deep URL, GT, and diagrammatic-backpropagation experiment artifacts.

Local only · curation required

software package

LINCS RADAR package ↗

Relational manifold, descent, chart-repair, and MovieLens studies.

Apache-2.0

← Return to the four-book sequenceTrace experiments to code →