In mathematics, specifically in category theory, an extranatural transformation[1] 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[2] (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.[2]
See also
References
External links
- extranatural+transformation at the nLab
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