A practical introduction to Category Theory
summary
A practical runthrough of Category Theory grounded in Scala: concrete Scala typeclass code lives on GitHub and is shown for Monoid, Functor, Applicative, Monad with pattern‑matching implementations for Maybe/Option, List and examples using addition/concatenation identities. Tests use Scalacheck to verify identity, composition and associativity. The talk demonstrates pure / ap / map / flatMap / flatten relations, explains applicatives as independent-box combination and monads as sequential chaining and monoids of endo‑functors.
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chapters (26)
- 0:00Start
- 3:04I AM NOT A MATHEMATICIAN
- 6:40WHAT IS A CATEGORY?
- 7:51COMPOSITION LAW
- 8:35COMPOSITION + ASSOCIATIVITY
- 10:26CATEGORY WITH 1 OBJECT
- 10:59MONOID'S RULES
- 11:19SCALACHECK FTW!
- 11:56A PRACTICAL EXAMPLE
- 13:45MONOID INSTANCES (1)
- 14:59CATEGORY WITH 1+ OBJECT
- 15:31CATEGORY IN A BOX
- 16:16LIFTING: CONTEXT VS CONTENT
- 17:11EXAMPLE OF BOXES
- 17:47FUNCTOR'S RULES
- 20:00FUNCTOR FOR MAYBE
- 21:14BOX FUNCTION + BOX VALUES
- 24:37APPLICATIVE FOR MAYBE
- 25:18BOX IN A BOX
- 26:53MONAD (AS FUNCTOR)
- 28:28BOXES IN A SEQUENCE
- 29:02FOR-COMPREHENSION
- 29:41MONAD (AS APPLICATIVE)
- 30:30MONAD FOR MAYBE
- 33:42SUMMARY
- 36:10WANNA KNOW MORE?
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