Category Theory - Part 1 of 6
summary
Course introduces concrete definitions and verifies the claims: sets and functions, identity, initial/terminal objects, universal property axiomatizes products, coproducts and exponentials; product is the set of pairs with projections and a unique pairing function Q from any X, coproduct is disjoint union with injections, exponential is the set of functions (2^3 = 8 example) and yields the currying isomorphism Hom(A×B,C) ≅ Hom(A,C^B). Examples use finite sets, diagrams and explicit constructions; existence and uniqueness are shown.
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chapters (12)
- 0:00Intro
- 3:02Prior Knowledge
- 4:51What is Category Theory
- 6:30Category of Sets
- 9:10Identity
- 12:22Initial Set
- 21:34Usefulness
- 24:58Universal Properties
- 30:52Asking Questions
- 38:21Example
- 50:21Exponentials
- 55:35Currying
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