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词条 Extranatural transformation
释义

  1. Definition

  2. Properties

  3. See also

  4. External links

  5. References

{{Short description|Generalization of natural transformations}}

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, of which they are a special case.[2]

See also

  • Dinatural transformation

External links

  • {{nlab|id=extranatural+transformation}}

References

1. ^Eilenberg and Kelly, A generalization of the functorial calculus, J. Algebra 3 366–375 (1966)
2. ^1 Fosco Loregian, This is the (co)end, my only (co)friend, arXiv preprint [https://arxiv.org/abs/1501.02503]

1 : Higher category theory
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