Taking the concrete example of

\\[ \mathbb{Z}_2[n \mod 2, b] \leftrightarrow \mathbb{N}[n, \iota(b)], \\]

we get,

\\[
\begin{matrix}
\mathbb{N} & \overset{- \mod 2}\rightarrow & \mathbb{Z}\_2\\\\
s\downarrow & & \downarrow \neg\\\\
\mathbb{N} & \underset{\iota}\leftarrow & \mathbb{Z}\_2
\end{matrix}
\\]

The induced functor \\(\iota \circ \neg \circ (- \mod n) \\) then sends even numbers to \\(0\\) in \\(\mathbb{N}\\) and odd numbers to \\(1\\) in \\(\mathbb{N}\\). This functor is a monad.