Noun
(mathematics) A related function that, given the output of the original function returns the input that produced that output.
In order for a function to have a left inverse it must be injective.
(category theory) For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that
s
∘
f
=
id
X
{\displaystyle s\circ f={\mbox{id}}_{X}}
.