In mathematics, specifically in category theory, an extranatural transformationEilenberg and Kelly, A generalization of the functorial calculus, J. Algebra 3 366–375 (1966) 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 endsFosco Loregian, This is the (co)end, my only (co)friend, arXiv preprint (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
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