Nonmapping

Nonmapping is a term used in multiple disciplines to refer to the absence or failure of a mapping between two structures, such as sets, spaces, or schemas. It is usually contrasted with a mapping or function, which assigns exactly one output in the codomain to every input in the domain.

In mathematics, a mapping is a rule that assigns to each element of a domain a single element of a codomain. A nonmapping describes a situation where this condition fails. This includes partial functions, where the rule is undefined for some inputs; multivalued mappings or relations, where a given input relates to several outputs; and more general correspondences that are not function-like. In category theory one would speak of a morphism; a nonmapping would be a non-morphism in that sense.

In computing and data science, nonmapping may describe the lack of a defined correspondence between fields in different schemas or data models. When data from a source cannot be transformed to fit a target structure, these fields are said to be non-mapped. Resolution strategies include schema augmentation, default values, or explicit transformation rules that realize the required mapping.

See also: mapping, function, relation, partial function, multivalued function, morphism, schema mapping.