Across the four-book sequence

10 ideas.
95 chapters.

Each route below follows one recurring question from categorical foundations through structural learning to controlled theory change. Chapter names and page locations come directly from the audited PDF outlines.

Route 01

Categorical language

What mathematical language makes composition, models, and structural promises explicit?

Categories for AGI develops the broad vocabulary; LINCS turns that vocabulary into axioms for structural learning; Infinitesimal Creativity adapts it to theory change.

Categories for AGI

  1. Chapter 1: Category Theory for AGIp. 23
  2. Chapter 2: Functors for AGIp. 31
  3. Chapter 3: Representable Functors and the Yoneda Lemmap. 43
  4. Chapter 4: Diagrams and Universal Constructionsp. 49

Machine Learning from Enforcing Compositionality

  1. Chapter 0: A Working Language of Compositionalityp. 33
  2. Chapter 1: Axioms of Structural Learningp. 59

Infinitesimal Creativity

  1. Chapter 0: A Working Language for Creative Theory Changep. 25
  2. Chapter 5: Algebraic Theories as Creative Targetsp. 107

Discovering Compositional Worlds from Interaction

  1. Chapter 1: A Categorical and Homotopical Toolkitp. 39
  2. Chapter 2: The ORACLE Programp. 65
  3. Chapter 3: Categorical Identification Under a Priorp. 77

Route 02

Compositional learning

How can a failure of composition become a typed signal for learning?

The sequence moves from diagrammatic backpropagation to sketches, factorization obstructions, localization, repair, and admission.

Categories for AGI

  1. Chapter 5: Categorical Deep Learningp. 59
  2. Chapter 6: Diagrammatic Backpropagationp. 69
  3. Chapter 8: Dynamic Compositionalityp. 95

Machine Learning from Enforcing Compositionality

  1. Chapter 2: Learning by Repairp. 75
  2. Chapter 3: Learning Sketches and Factorization Obstructionsp. 83
  3. Chapter 4: Tangent Learning Sketchesp. 91
  4. Chapter 8: Deep Learning in Non-Compositional Sketchesp. 133
  5. Chapter 9: Quotients, Localization, Repair, and Admissionp. 143

Infinitesimal Creativity

  1. Chapter 2: Creativity as Theory Constructionp. 53
  2. Chapter 10: DIAL as an Algorithmic Familyp. 175

Discovering Compositional Worlds from Interaction

  1. Chapter 5: Learning Inside Fixed Doctrinesp. 109
  2. Chapter 6: The UOCL Machinep. 139
  3. Chapter 7: Persistent Categorical Identificationp. 151
  4. Chapter 8: Probably Approximately Categorically Correct Learningp. 159

Route 03

Sketches and theories

How are domain theories declared, acquired, extended, and transported?

Sketches progress from presentations of compositional structure to learned declarations and finite theory extensions.

Categories for AGI

  1. Chapter 4: Diagrams and Universal Constructionsp. 49

Machine Learning from Enforcing Compositionality

  1. Chapter 0: A Working Language of Compositionalityp. 33
  2. Chapter 1: Axioms of Structural Learningp. 59
  3. Chapter 3: Learning Sketches and Factorization Obstructionsp. 83
  4. Chapter 9: Quotients, Localization, Repair, and Admissionp. 143
  5. Chapter 21: A Pattern Language for LINCS Systemsp. 243

Infinitesimal Creativity

  1. Chapter 0: A Working Language for Creative Theory Changep. 25
  2. Chapter 1: Initial Sketch Acquisitionp. 41
  3. Chapter 2: Creativity as Theory Constructionp. 53
  4. Chapter 5: Algebraic Theories as Creative Targetsp. 107

Discovering Compositional Worlds from Interaction

  1. Chapter 0: The Infant's Problemp. 25
  2. Chapter 1: A Categorical and Homotopical Toolkitp. 39
  3. Chapter 2: The ORACLE Programp. 65
  4. Chapter 5: Learning Inside Fixed Doctrinesp. 109
  5. Chapter 16: Persistent Structure Across a Lifetimep. 255

Route 04

Infinitesimal geometry

What becomes observable when models and theories are probed through tangent structure?

Tangent lifts, infinitesimal databases, decision structure, and double involution supply local geometry for diagnosis and controlled theory change.

Categories for AGI

  1. Chapter 12: Manifold Learning with Geometric Transformersp. 183
  2. Chapter 25: Causal Density Functionsp. 397

Machine Learning from Enforcing Compositionality

  1. Chapter 4: Tangent Learning Sketchesp. 91
  2. Chapter 5: Infinitesimal Causalityp. 101
  3. Chapter 6: Infinitesimal Categorical Databasesp. 111
  4. Chapter 7: Infinitesimal Decisionsp. 123
  5. Chapter 8: Deep Learning in Non-Compositional Sketchesp. 133

Infinitesimal Creativity

  1. Chapter 3: The Differential Geometry of Creativityp. 65
  2. Chapter 4: Skill Optimization for Creative Explorationp. 93

Discovering Compositional Worlds from Interaction

  1. Chapter 1: A Categorical and Homotopical Toolkitp. 39
  2. Chapter 7: Persistent Categorical Identificationp. 151
  3. Chapter 14: Homotopy and Tangent Repairp. 237

Route 05

Causality and intervention

How do observation, intervention, latent structure, and active experiments interact?

Categorical causal models lead to infinitesimal diagnosis, geometric causal discovery, and theory extension grounded by simulators or scientific evidence.

Categories for AGI

  1. Chapter 15: Adjoint Functorsp. 207
  2. Chapter 19: Topos Causal Modelsp. 257
  3. Chapter 20: Judo Calculusp. 269
  4. Chapter 21: Csql: Mapping Documents into Topos Causal Model Databasesp. 305
  5. Chapter 25: Causal Density Functionsp. 397

Machine Learning from Enforcing Compositionality

  1. Chapter 5: Infinitesimal Causalityp. 101
  2. Chapter 11: Geometric Causal Discoveryp. 165
  3. Chapter 12: Repairing Kan-Extension Structurep. 173

Infinitesimal Creativity

  1. Chapter 11: Causal Learning with Infinitesimal Creativityp. 197
  2. Chapter 16: Simulator-Grounded Theory Extensionp. 285
  3. Chapter 17: From Scientific Documents to Testable Theoriesp. 303

Discovering Compositional Worlds from Interaction

  1. Chapter 3: Categorical Identification Under a Priorp. 77
  2. Chapter 5: Learning Inside Fixed Doctrinesp. 109
  3. Chapter 14: Homotopy and Tangent Repairp. 237

Route 06

Decisions and reinforcement learning

How can sequential behavior be represented beyond one fixed decision formalism?

Universal decision models and infinitesimal decision structure culminate in RELIC and the DIAL–URL theory-construction testbed.

Categories for AGI

  1. Chapter 26: Universal Decisions with Kan Extensionsp. 409
  2. Chapter 27: Universal Reinforcement Learningp. 423
  3. Chapter 28: Deep URL with Geometric Transformersp. 427

Machine Learning from Enforcing Compositionality

  1. Chapter 7: Infinitesimal Decisionsp. 123
  2. Chapter 15: Infinitesimal Reinforcement Learningp. 193
  3. Chapter 16: Learning from Structured Preferencesp. 203

Infinitesimal Creativity

  1. Chapter 13: Reinforcement Learning with Infinitesimal Creativityp. 219
  2. Chapter 15: Mathematical Theory Constructionp. 251

Discovering Compositional Worlds from Interaction

  1. Chapter 9: Online and Persistent Universal Decision Learningp. 171
  2. Chapter 10: Convex and Regularized Universal Actionp. 201
  3. Chapter 11: Universal Bandit Decision Learningp. 211
  4. Chapter 12: Information Categories and Decentralized Decisionsp. 219

Route 07

Reasoning and assurance

How can reasoning steps, repairs, and system claims remain inspectable?

Agent construction, formal companions, structural reasoning, and trustworthy foundation models provide progressively stronger audit boundaries.

Categories for AGI

  1. Chapter 18: Building Agentic Systems using Kan Extension Transformersp. 243
  2. Chapter 31: Formal Verification Mapp. 445
  3. Chapter 32: CLIFF Companionp. 451
  4. Chapter 33: Code Companionp. 459

Machine Learning from Enforcing Compositionality

  1. Chapter 10: Reasoning by Structural Repairp. 153
  2. Chapter 19: Infinitesimal Argument Repairp. 223
  3. Chapter 20: Trustworthy Foundation Modelsp. 229

Infinitesimal Creativity

  1. Chapter 14: Composing Creative Workflowsp. 235
  2. Chapter 17: From Scientific Documents to Testable Theoriesp. 303

Discovering Compositional Worlds from Interaction

  1. Chapter 8: Probably Approximately Categorically Correct Learningp. 159
  2. Chapter 13: Agentic Safety and Universal Online Decision Learningp. 227
  3. Chapter 14: Homotopy and Tangent Repairp. 237
  4. Chapter 17: Synthesis and the Next ORACLE Theorem Ladderp. 263

Route 08

Scientific discovery

How can evidence drive the construction, revision, and testing of scientific theories?

The program separates pattern discovery from causal explanation, experimental admission, and the design of sustained research programs.

Categories for AGI

  1. Chapter 16: Causal Claims from Languagep. 213
  2. Chapter 17: Temporal Diffusion over Causal Trajectoriesp. 221
  3. Chapter 21: Csql: Mapping Documents into Topos Causal Model Databasesp. 305

Machine Learning from Enforcing Compositionality

  1. Chapter 22: Frontiers of Infinitesimal Learningp. 247

Infinitesimal Creativity

  1. Chapter 6: Landscapes of Computational Creativityp. 123
  2. Chapter 15: Mathematical Theory Constructionp. 251
  3. Chapter 16: Simulator-Grounded Theory Extensionp. 285
  4. Chapter 17: From Scientific Documents to Testable Theoriesp. 303

Discovering Compositional Worlds from Interaction

  1. Chapter 0: The Infant's Problemp. 25
  2. Chapter 5: Learning Inside Fixed Doctrinesp. 109
  3. Chapter 16: Persistent Structure Across a Lifetimep. 255
  4. Chapter 17: Synthesis and the Next ORACLE Theorem Ladderp. 263

Route 09

Visual generation and repair

How can a visual system enforce scene theories and eventually invent reusable generative operations?

ARTISTIC diagnoses and repairs declared visual constraints; DILATE poses the harder problem of admitting reusable extensions to the generative process itself.

Infinitesimal Creativity

  1. Chapter 18: Generative Visual Languagesp. 349
  2. Chapter 19: Artistic Theory Extensionp. 385

Discovering Compositional Worlds from Interaction

  1. Chapter 5: Learning Inside Fixed Doctrinesp. 109
  2. Chapter 16: Persistent Structure Across a Lifetimep. 255

Route 10

Doctrines and categorical identification

How can a learner discover not only a model, but the kind of compositional world in which that model lives?

The fourth volume makes the categorical prior explicit: assimilation learns within a doctrine, while accommodation may revise the doctrine itself.

Categories for AGI

  1. Chapter 1: Category Theory for AGIp. 23
  2. Chapter 4: Diagrams and Universal Constructionsp. 49

Machine Learning from Enforcing Compositionality

  1. Chapter 0: A Working Language of Compositionalityp. 33
  2. Chapter 1: Axioms of Structural Learningp. 59
  3. Chapter 3: Learning Sketches and Factorization Obstructionsp. 83

Infinitesimal Creativity

  1. Chapter 2: Creativity as Theory Constructionp. 53
  2. Chapter 3: The Differential Geometry of Creativityp. 65
  3. Chapter 5: Algebraic Theories as Creative Targetsp. 107

Discovering Compositional Worlds from Interaction

  1. Chapter 1: A Categorical and Homotopical Toolkitp. 39
  2. Chapter 2: The ORACLE Programp. 65
  3. Chapter 3: Categorical Identification Under a Priorp. 77
  4. Chapter 4: Core Knowledge and Piagetian Constructionp. 89
  5. Chapter 6: The UOCL Machinep. 139
  6. Chapter 17: Synthesis and the Next ORACLE Theorem Ladderp. 263
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