Category Theory as a Tool for Thought
summary
Argues that category theory yields concrete programmatic payoff by defining types and abstractions via relationships and then applying mechanical transforms: rewrites of product diagrams produce coproducts via duality, limits and cones become universal constructions that recover unit/void and products, the initial-object construction produces the free monoid (lists) and a path through the comma category explains how arbitrary functions factor through homomorphisms, and those constructions port to the category of endofunctors to give free monads and generic folds.
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chapters (16)
- 0:00Intro
- 1:34Exploring the idea Space
- 3:23Outline
- 4:57Category Theory 101
- 5:27The Category of Types
- 7:31What's in a Tuple
- 12:08Universal Constructions
- 13:00Diagrams and Limits
- 16:01Initial and Terminal Objects
- 19:51The Monoid Category
- 21:17Memories of Homomorphisms Past
- 23:37Exploration
- 28:46Monoids Redux
- 30:34The Category of Endefunctors
- 34:47Case Study
- 36:08The Tools for Thought
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