Multisets are containers, also called bags. A multiset is a set that can have repeats:
$$\{ a, a, a, c, b, c \}$$
Usually when researchers talk about multisets, they use this kind of presentation:
$$ \psi = 3| a \rangle + 2| c \rangle + | b \rangle $$
In fact, $\psi$ is actual an element of an $\mathbb{N}$-module. $\mathbb{N}$-modules are the Eilenberg-Moore category of the multiset monad. Why do researchers always represent multisets as $\mathbb{N}$-modules? What is the deep implication here?