What Is a Monoid?

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Proposes a two-stage generalization of multicategories that actually makes sequencing and relative-monad examples into monoids: first left-skew multicategory (captures forward and other relative monads), then the new bi-skew multicategory (captures call-by-push-value sequencing and categories on spans). Builds formal definitions, composes dozens of variant composition laws, and proves a coherence theorem that every monoid uniquely extends to an unbiased monoid (a map from the terminal bi-skew multicategory). The constructions and examples in section 5.4 validate the approach.

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" chapters (12)

1. 0:00Monoids in programming and math
2. 4:37Category theory basics
3. 8:32What is a monoid?
4. 11:18Limitations of multicategories
5. 14:04Left skew multicategories
6. 18:56Monoids in left skew
7. 20:00Bi skew multicategories
8. 21:26Monoids in bi skew
9. 22:29Coherence theorem
10. 23:10Operads and abstractions
11. 24:12Conclusion
12. 24:35Question and answer session