Let $A$ be the set of $26$ letters of the alphabet. Let $B$ be the numbers from $0$ to $25.$ A simple code might replace each letter with the number corresponding to its index in the list. The function from letters to their numbers would have type

$c$ :

A shift of $3$ in this code might add $3$ to each output wrapping around. This can be done with modular arithmetic as $s(i)=(i+3)mod26.$

What is the type of $s?$

$s$ :

The shifted code could be written as the following composition of $s$ and $c.$

$g=$

All of the functions described here are bijections. What is $s^{-1}?$

$s^{-1}(i)=i+,$mod