3.1 MonoidM (m, m)

Same meaning in Category as in Set: Only 1 object, Associative, Identity

**Thin / Thick Category**:

- “Thin” with only 1 arrow between 2 objects;
- “Thick” with many arrows between 2 objects.

**Arrow** : relation between 2 objects. We don’t care what an arrow actually is (may be total / partial order relations like = or $latex leq $, or any relation), just treat arrow abstractly.

Note: Category Theory’s “Abstract Nonsense” is like Buddhism “空即色, 色即空” (Form = Emptiness).

**Example of**Monoid: String Concatenation: identity = Null string.

**Strong Typing**: function f calls function g, both types must match.

**Weak Typing**: no need to match type. eg. Monoid.

Category induces a Hom-Set: (Set of “Arrows”, aka

Homomorphism同态, whichpreserves structureafter the “Arrow”)

- C (a, b) : a -> b
- C (a,a) for Monoid…

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