Extranatural transformation
In mathematics, specifically in category theory, an extranatural transformation[1] is a generalization of the notion of natural transformation.
Definition
Let and
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.[2]
See also
External links
References
- ↑ Eilenberg and Kelly, A generalization of the functorial calculus, J. Algebra 3 366–375 (1966)
- 1 2 Fosco Loregian, This is the (co)end, my only (co)friend, arXiv preprint
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