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Modification (mathematics)

In mathematics, specifically category theory, a modification is an arrow between natural transformations. It is a 3-cell in the 3-category of 2-cells (where the 2-cells are natural transformations, the 1-cells are functors, and the 0-cells are categories). The notion is due to Bénabou.

Given two natural transformations , there exists a modification such that:

  • ,
  • , and
  • .

The following commutative diagram shows an example of a modification and its inner workings.

References