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mwaaas/Category-Theory-for-AGI-UMass-CMPSCI-692CT

Sample Google Colab code to illustrate application of category theory to AGI

Category Theory for AGI — Colab Course Template

This bundle contains Colab-ready notebooks with a consistent Environment cell,
lightweight micro-demos, and exercises. Push this repo to GitHub and replace sridharmahadevan/Category-Theory-for-AGI-UMass-CMPSCI-692CT
in each badge so students can launch directly in Colab.

Structure

  • notebooks/week01_backprop_as_functor.ipynb
  • notebooks/week01_sudoku_gt_db.ipynb (Sudoku GT vs Transformer + Diagrammatic Backprop)
  • notebooks/week01_lm_gt_vs_transformer.ipynb (PTB language modeling: GT vs Transformer)
  • notebooks/week01_coalgebra_demo.ipynb (Coalgebra: deterministic + MDP)
  • notebooks/week02_yoneda_microdemo.ipynb
  • notebooks/week02_yoneda_self_attention_demo1.ipynb (Yoneda self-attention demo)
  • notebooks/week03_limits_colimits_microdemo.ipynb
  • notebooks/week03_db_colimit_energy.ipynb (DB as (co)limit energy minimization)
  • notebooks/week04_clustering_as_functor.ipynb
  • notebooks/week04_gt_full_node_labeling.ipynb (GT‑Full toy node labeling)
  • notebooks/week05_mini_democritus.ipynb (Mini‑Democritus causal manifold)
  • notebooks/week06_gt_full_ptb.ipynb (GT‑Full on PTB, tiny LM)
  • notebooks/week07_sheaves_covers.ipynb (Sheaves via covers and gluing)
  • notebooks/week08_topos_overlap_penalty.ipynb (Topos overlap consistency penalty)
  • notebooks/week09_causal_discovery_toy.ipynb (Toy causal discovery)
  • notebooks/week10_kan_do_rn.ipynb (Kan-Do calculus with RN ratios)
  • notebooks/week11_subobject_classifier.ipynb (Subobject classifier in Sets)
  • notebooks/week12_jstability_regimes.ipynb (j-stability across regimes)
  • notebooks/week13_democritus_manifold.ipynb (Democritus causal manifold demo)
  • notebooks/week13_open_games_attention_economy.ipynb (Open games: attention economy)
  • data/democritus/manifold.npz (small topic manifold snapshot)

Usage

  1. Open the notebook link (or upload to Colab), run the Environment cell first.
  2. GPU is optional. All examples run on CPU in < 5 minutes.
  3. For local use, create a conda env via environment.yml and run JupyterLab.

Colab Badge Template

[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)]
(https://colab.research.google.com/github/sridharmahadevan/Category-Theory-for-AGI-UMass-CMPSCI-692CT/blob/main/notebooks/week01_backprop_as_functor.ipynb)

Replace sridharmahadevan/Category-Theory-for-AGI-UMass-CMPSCI-692CT once you publish the repo.

Local environment (optional)

conda env create -f environment.yml
conda activate ct4agi
jupyter lab

Colab Badges

  • Week 1 — Backprop as a Functor
    Functorial view of backprop with a small, runnable micro-demo.
    Open In Colab
  • Week 1 — Sudoku GT + Diagrammatic Backprop
    Compare Geometric Transformer vs. baseline Transformer on 4x4 Sudoku; optional DB curvature penalty.
    Open In Colab
  • Week 1 — Language Modeling (PTB): GT vs Transformer
    Compare Geometric Transformer vs. baseline Transformer on a tiny PTB language model.
    Open In Colab
  • Week 1 — Coalgebra Demo
    Deterministic system + MDP as coalgebras.
    Open In Colab
  • Week 2 — Yoneda Micro-Demo
    Open In Colab
  • Week 2 — Yoneda Self-Attention Demo 1
    Open In Colab
  • Week 3 — Limits & Colimits Micro-Demos
    Open In Colab
  • Week 3 — DB as (Co)limit Energy
    Minimize consistency/gluing energy to approximate limits and colimits.
    Open In Colab
  • Week 4 — Clustering as a Functor
    Open In Colab
  • Week 4 — GT‑Full Toy Node Labeling
    Relation‑aware GT‑Full message passing vs baseline MLP.
    Open In Colab
  • Week 5 — Mini‑Democritus
    Causal triples → GT‑Full embeddings → 2D manifold.
    Open In Colab
  • Week 6 — GT‑Full on PTB (Tiny)
    Relation‑aware GT‑Full LM vs baseline Transformer on PTB.
    Open In Colab
  • Week 7 — Sheaves via Covers and Gluing
    Local covers + overlap consistency on a toy interference example.
    Open In Colab
  • Week 8 — Topos Overlap Penalty
    Sheaf-style overlap penalty prefers the true causal graph.
    Open In Colab
  • Week 9 — Toy Causal Discovery
    Recover edges from a linear SEM with simple regressions.
    Open In Colab
  • Week 10 — Kan-Do Calculus with RN Ratios
    Conditioning vs intervention via Radon–Nikodym reweighting.
    Open In Colab
  • Week 11 — Subobject Classifier
    Characteristic maps in Sets as a concrete subobject classifier.
    Open In Colab
  • Week 12 — j-Stability Across Regimes
    Stable edges across environments from synthetic SEMs.
    Open In Colab
  • Week 13 — Democritus Causal Manifold
    Visualize a topic manifold as a lightweight DB + GT example.
    Open In Colab
  • Week 13 — Open Games: Attention Economy
    Simple open‑game play/co‑play demo for attention competition.
    Open In Colab

Languages

Jupyter Notebook100.0%

Contributors

SR
Apache License 2.0
Created February 9, 2026
Updated February 9, 2026
mwaaas/Category-Theory-for-AGI-UMass-CMPSCI-692CT | GitHunt