COMPSCI 692CT — Category Theory for AGI
Meets Mon/Wed 5:30–6:45pm ET · Online (live & recorded) · Instructor: Sridhar Mahadevan · Zoom link: contact me
What is this course about?
The world's largest AI companies are collectively spending several trillion dollars in the most expensive race in human history to build artificial general intelligence (AGI). This course will give students a detailed introduction to category theory, and how to use it to analyze today’s AGI systems, understand their limitations and how to design the next generation of AGI sytems. We’ll cover the core theoretical concepts, including categories, functors, natural transformations, the Yoneda lemma, limits & colimits, adjunctions, monads, and Kan extensions, as well as their application to building AGI systems that can reason causally, learn from their experience, plan to achieve long-term goals, interact with users in natural language, and ultimately, achieve consciousness. Broadly, the first 7 weeks of the course will present the Yoneda viewpoint: behavioral equivalence is sufficient for AGI (the "attention is all you need" perspective). Weeks 7 through 14 will cover the topos theory perspective: consciousness is crucial for AGI, which requires logical reasoning in a topos through maintaining local truths via a subobject classifier.
Texts
- Primary: Emily Riehl, Category Theory in Context (Dover, 2016). Download Emily Riehl's book
- Primary: Sridhar Mahadevan, Categories for AGI (2026). Free PDF hosted by the author: Download Categories for AGI book
GitHub Repository
- Sample Code will be available here and updated periodically: GitHub Repository
Tentative weekly outline
| Week | Category Theory Focus | Slides |
|---|---|---|
| W1 | Categories & Functors | Lecture 1, Lecture 2 |
| W2 | Natural Transformations & Yoneda Lemma | Lecture 3, Lecture 4 |
| W3 | Limits & Colimits | Lecture 5, Lecture 6 |
| W4 | Adjunctions | Geometric Transformers |
| W5 | Monads | Categorical Probability and Disintegration |
| W6 | Symmetric Monoidal Categories | Markov Categories and string diagrams |
| W7 | Topos Theory | New Architectures for LLMs |
| W8 | Presheaves & Internal Logic (Ω) | Reasoning in possible worlds |
| W9 | Topos Causal Models I | Interventions as Subobject Clasifiers |
| W10 | Kan Extensions | Learning to Extend Functors |
| W11 | Coalgebras & Coinduction | Universal Reinforcement Learning |
| W12 | Simplicial Sets | UMAP and manifold learning |
| W13 | Compositional Games | Equilibria via variational inequalities |
| W14 | Consciousness And Student Project Demos | Frontiers of AGI |
This outline will evolve; readings and Zoom link will appear here.
Contact
Instructor: Sridhar Mahadevan · Email: mahadeva@cs.umass.edu
© 2026 UMass Amherst · COMPSCI 692CT