Extranatural transformation
In mathematics, specifically in category theory, an extranatural transformation is a generalization of the notion of natural transformation. Definition
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:
 is a natural transformation (in the usual sense). (extranaturality in b) , ,  the following diagram commutes

 

 (extranaturality in c) , ,  the following diagram commutes

Properties 
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. See also 
 Dinatural transformation

References

External links 
 

Higher category theory