Associativity

Any associative operation $\otimes$ satisfies the law

$$(a \otimes b) \otimes c = a \otimes (b \otimes c)$$

In short, that the operands can be associated in any order.

Backlinks

• A monoid has an associative binary operation
  • Any monoid has an associative binary operation that takes any two elements in the associated set and produces an element in that set.
• The composition of morphisms in a monoidal category corresponds to an associative binary operation
  • Composing any two of these morphisms corresponds to performing the operation - the operation is associative because composition of morphisms is associative.