Computational Exploration of Finite Semigroupoids

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Relational programs (miniKanren via core.logic) implement a package called Ken that enumerates finite semigroupoids as partial composition tables, constructs homomorphisms (strict vs permissive), and searches for minimal transformation representations; associativity and consistent typing turn out to be independent, and arrow-type semigroupoids are enumerated (sequence absent from OEIS). A flip‑flop semigroup example is rebuilt concretely, enumeration and isomorphism checking runs take about two weeks on naive search.

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" chapters (15)

1. 0:00Computational exploration intro
2. 1:06Semigroup to category theory
3. 2:33Defining semigroupoids
4. 5:47Key questions on finite semigroupoids
5. 7:12Introducing Ken tool
6. 7:54Enumerating semigroups with Ken
7. 10:33Challenges in enumeration
8. 13:25Type structure inference
9. 15:20Empty composition demo
10. 16:25Structure-preserving morphisms
11. 18:12Arrow-type semigroupoids
12. 19:17Transformations and automata
13. 20:42Enumeration results
14. 22:05Reflections on core.logic
15. 23:09Conclusion and Q&A