Dinatural transformation

In category theory, a branch of mathematics, a dinatural transformation

$\alpha$

between two functors

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

written

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

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

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

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

commutes. Note the direction of $S(f,g)$ is opposite along $f$ in the first component since it is contravariant.

The composition of two dinatural transformations need not be dinatural.

See also

• Extranatural transformation
• Natural transformation

External links

• dinatural transformation at the nLab