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.
- A monoid has an associative binary operation
- 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.