Category Theory - Part 4 of 6

on YouTube ↗01h 00m

" summary

Part 4 gives concrete translations rather than abstract slogans: it shows functors to Set as databases by writing the tables for vertices and arrows, proves graphs = functors from a two‑object indexing category and that natural transformations = graph (database) homomorphisms via the commuting source/target squares, works the safeHead example as a naturality check, and sketches adjoints and currying with a product/currying example; mentions an open‑source query tool to try these ideas interactively.

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" chapters (14)

1. 0:00Start
2. 7:38Natural Transformations
3. 7:55The Natural Transformation
4. 16:52Category Theory of Primordial Ooze
5. 28:06Respecting Source and Target
6. 29:41Graph Homomorphism
7. 30:00Database Homomorphism
8. 33:02Maps between Functors
9. 38:09Algebraic Databases
10. 45:50Disjoint Union
11. 48:29Review Natural Transformations
12. 49:39Naturality Condition
13. 52:25Adjoint Ad Junctions
14. 55:30Natural Isomorphism

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