Category Theory - Part 2 of 6
summary
Explains why Universal Properties, not implementations, uniquely characterize constructions: shows how an evaluation map EV and the exponential object are defined and tested (counterexamples: constant or random EV fail); models examples concretely — Set and Hask, discrete categories, posets as categories, monoids as one‑object categories — and builds the free category on a graph; sketches algebraic databases as finitely presented categories and how products, coproducts, initials and terminals are checked by the universal property.
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chapters (18)
- 0:00Intro
- 1:48The world is consistent
- 3:05Communication at scale
- 8:35Identity
- 9:05Notation
- 12:30For all
- 17:45What is a category
- 19:03Class
- 21:53Sets
- 24:33Category
- 29:28Discrete Category
- 31:53Partially Ordered Sets
- 34:53Post Sets
- 39:53Equality and Evil
- 43:53Three Dogs
- 44:53Categories
- 49:48Monoid
- 52:43AB M
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