Extranatural transformation

In mathematics, specifically in category theory, an extranatural transformation is a generalization of the notion of natural transformation.

Let ${\displaystyle F:A\times B^{\mathrm {op} }\times B\rightarrow D}$ and ${\displaystyle G:A\times C^{\mathrm {op} }\times C\rightarrow D}$ two functors of categories. A family ${\displaystyle \eta (a,b,c):F(a,b,b)\rightarrow G(a,c,c)}$ is said to be natural in a and extranatural in b and c if the following holds:

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