Split-octonion

In category theory, a dinatural transformation $\alpha$ between two functors

$S,T:C^{\mathrm{o}\mathrm{p}}\times C\to X,$

written

$\alpha :S\ddot{\to }T,$

is a function which to every object c of C associates an arrow

${\alpha }_c:S(c,c)\to T(c,c)$ of X

and satisfies the following coherence property: for every morphism $f:c\to c^{\prime }$ of C the diagram

File:Dinatural transfo1.png

commutes.

The composition of two dinatural transformations need not be dinatural.

External links

• dinatural transformation at the n-Category Lab.

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