Scale By The Bay 2018 Unconference: Runar Bjarnason
summary
Starts from plain functions and builds category theory step by step, formalizing composition and identity then instantiating them: Scala subtype category (types as objects, subtyping as arrows), posets as single-arrow-or-none categories, and monoid as one-object category (elements as arrows). Defines functors and endofunctors, shows List endofunctor and how map preserves composition, then explains natural transformations as a polymorphic family of arrows—natural transformation = polymorphic family—that must make commutative diagrams and preserve structure.
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chapters (9)
- 0:00Introduction to category theory
- 4:11Functions as categories
- 10:35Examples of categories
- 17:26Monoids as categories
- 26:47Discrete and small categories
- 27:07Functors explained
- 33:25Category of categories
- 36:22Endofunctors and natural transformations
- 45:42Q&A and summary
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