Given a map between sets and , the map is called a right inverse to provided that , that is, composing with from the right gives the identity on . Often is a map of a specific type, such as a linear map between vector spaces, or a continuous map between topological spaces, and in each such case, one often requires a right inverse to be of the same type as that of .
If has a right inverse, then is surjective. Conversely, if is surjective and the axiom of choice is assumed, then has a right inverse, at least as a set mapping.
between sets 
and 
, the map 
is called a right inverse to 
provided that 
, that is, composing 
with 
from the right gives the identity on 
. Often 
is a map of a specific type, such as a linear map between vector spaces, or a continuous map between topological spaces, and in each such case, one often requires a right inverse to be of the same type as that of 
. 
has a right inverse, then 
is surjective. Conversely, if 
is surjective and the axiom of choice is assumed, then 
has a right inverse, at least as a set mapping. 