Monoidal Identity

The monoidal identity is the identity value for a particular monoid. A monoid must have an identity value and an associative binary operation. The identity value $m$ is a value which makes no change to any other value $n$ in that monoid, when $n$ is combined with $m$ using that binary operation.

$1$ is the monoidal identity for natural numbers under multiplication. $1 \cdot n = n \cdot 1 = n$. $0$ is the monoidal identity for natural numbers under addition. $0 + n = n + 0 = n$

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• Monoid
  • A monoid is an algebraic structure with an identity value and an associative binary operation.
• Product Type
  • Product types have a monoidal identity of Unit. $|Unit| = 1$.
• Sum Type
  • The monoidal identity of the sum operation is the void type, as $|Void| = 0$.