Let and be sets, and let be a function of variables: . Fix for . The induced mapping is called the partial mapping determined by corresponding to the first variable.

In the case where , the map defined by is often denoted . Further, any function determines a mapping from into the set of mappings of into , namely . The converse holds too, and it is customary to identify with . Many of the “canonical isomorphisms” that we come across (e.g. in multilinear algebra) are illustrations of this kind of identification.