I know that if for any set $U$, the power set of $U$ forms a monoid(a commutative one) under set union, because it is closed under the operation, is associative and it has an identity element $\emptyset$.
Following the argument that this is true for any set, it seems reasonable to think about the class of sets forming a monoid with $\emptyset$ as its identity, but, is it correct to say so? Or it must be a set even though there is a monoid for any set?
