Consider the following category: \(\boxed{\overset{\bullet}{z}\circlearrowleft s\ \ \boxed{s;s = s}}\)
A functor from this category to Set is a set \(Z\) and a involution function \(Z \rightarrow Z\).
\(Z =\) natural numbers and a function sending everything to zero (zero is sent to zero)
\(Z =\) set of well-formed arithmetic expressions (e.g. \(12+(2*4)\)) and a function which evaluates to an integer (which itself is a well-formed expression). Evaluation on integers does nothing.
A function which sends numbers greater than 2 to their smallest prime factor (this is a no-op on the prime factors themselves).