In my opinion, requiring commutativity from a +-operator is maybe too much. Associativity and a neutral element seem to be enough (i.e. forming a monoid).
> requiring commutativity from a +-operator is maybe too much
The + operator is the only one that can be realistically required to be commutative. All other operators need not. If we are to have any commutative operator, it should definitely be +.
