Extranatural transformation

In mathematics, specifically in category theory, an extranatural transformation is a generalization of the notion of natural transformation.
Definition.
Let formula_1 and formula_2 two functors of categories.
A family formula_3 is said to be natural in "a" and extranatural in "b" and "c" if the following holds:
Properties.
Extranatural transformations can be used to define wedges and thereby ends (dually co-wedges and co-ends), by setting formula_13 (dually formula_14) constant.
Extranatural transformations can be defined in terms of dinatural transformations, of which they are a special case.