Category Theory - Part 6 of 6
summary
Defines Galois connections concretely: image and preimage forming a Galois connection for powersets. Shows adjunctions produce monads (unit and mu given by unit/co-unit) and gives concrete monads: list monad with singleton and flatten (join), maybe, and state (times A / A‑power). Constructs Kleisli composition so Kleisli category gives bind as composition, and Eilenberg–Moore (Islandburg–More) algebras as MC → C. Claims: every adjunction yields a monad; lists are the initial algebra for X ↦ A×X+1 and streams the final coalgebra.
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chapters (7)
- 0:00Start
- 5:34Galois Connections
- 7:25Power Sets
- 12:38Galois Connection
- 19:08Lists
- 41:24M Algebras
- 48:37Initial Algebra
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