What is the name two mutually idempotent functions? To clarify, in haskell, there is an ord function that gives the byte integer of a character (i.e. ord 'a' yields 97); and there is a char function that takes the byte integer of a character and returns the character (i.e. char 97 yelds 'a'.

What is the name of a collection of such functions? I'm not very mathematically literate (I'm working on it), but I found semirings on wikipedia. Do semirings provide an appropriate description?
These are known as inverse functions. For example, the mappings $x \mapsto 2x$ and $x \mapsto x/2$ are inverses of each other, as are $\exp$ and $\log$ (restricted to positive numbers), or $\sin$ (restricted to the interval $[-\pi/2,\pi/2]$) and $\arcsin$.