In mathematics, specifically in category theory, an extranatural transformation is a generalization of the notion of natural transformation.
Let and be two functors of categories. A family is said to be natural in a and extranatural in b and c if the following holds:
Extranatural transformations can be used to define wedges and thereby ends (dually co-wedges and co-ends), by setting (dually ) constant.
Extranatural transformations can be defined in terms of dinatural transformations, of which they are a special case.