Category Theory: An Abstraction for Anything
summary
Shows how a concrete git commit DAG becomes a category (objects = commits, morphisms = reachability), defines initial/terminal objects, and implements examples in Scala. Builds functors (forgetful, Option, List), demonstrates a concrete option → list natural transformation that makes diagrams commute, and derives currying from Hom functors as another natural transformation with an isomorphism. Includes code sketches, diagram chases, and type-signature reasoning to show these constructions actually compose and behave as claimed.
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chapters (12)
- 0:00Start
- 0:17TALK OUTLINE
- 0:43DIRECTED ACYCLIC GRAPHS
- 2:15CREATING A CATEGORY
- 5:15TERMINAL AND INITIAL OBJECTS
- 7:15CATEGORY OF ALL THE GRAPHS
- 9:06FORGETFUL FUNCTOR
- 11:02OPTION FUNCTOR
- 14:39POLYMORPHIC FUNCTIONS
- 16:03NATURAL TRANSFORMATIONS
- 29:20COMIC INTERLUDE
- 29:37CURRYING
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