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 ofMonoid: 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, which preserves structure after the “Arrow”)
- C (a, b) : a -> b
- C (a,a) for Monoid…
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