by Daniel Sinderson
This is course 2B in my DIY graduate program. It’s a year-long course in applied category theory and the basics of higher dimensional category theory, in particular double categories and their applications.
The primary texts will be Seven Sketches in Compositionality by Brendan Fong and David Spivak and the first half of Higher Dimensional Categories by Marco Grandis.
| # | Chapter | HW | Lab |
|---|---|---|---|
| 1 | Generative Effects: Orders and Galois Connections | Notes | |
| 2 | Problem Sets | ||
| 3 | Resource Theories: Monoidal Preorders and Enrichment | Notes | |
| 4 | Problem Sets | ||
| 5 | Databases: Categories, Functors, and Universal Constructions | Notes | |
| 6 | Problem Sets | ||
| 7 | Collaborative Design: Profunctors, Categorification, and Monoidal Categories | Notes | |
| 8 | Problem Sets | ||
| 9 | Signal Flow Graphs: Props, Presentations, and Proofs | Notes | |
| 10 | Problem Sets | ||
| 11 | Electric Circuits: Hypergraph Categories and Operads | Notes | |
| 12 | Problem Sets | ||
| 13 | Logic of Behavior: Sheaves, Toposes, and Internal Languages | Notes | |
| 14 | Problem Sets | ||
| 15 | Notes | ||
| 16 | A Review of Basic Category Theory | Problem Sets | |
| 17 | Notes | ||
| 18 | Problem Sets | ||
| 19 | Introducing Two-Dimensional Category Theory | Notes | |
| 20 | Problem Sets | ||
| 21 | Notes | ||
| 22 | Double Categories | Problem Sets | |
| 23 | Notes | ||
| 24 | Problem Sets | ||
| 25 | Double Adjunctions | Notes | |
| 26 | Problem Sets | ||
| 27 | Notes | ||
| 28 | Double Limits | Problem Sets | |
| 29 | Notes | ||
| 30 | Problem Sets |
Written on: December 1, 2024