Dinatural transformation

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

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

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 $f:c\to c'$ of $C$ the diagram

commutes.

The composition of two dinatural transformations need not be dinatural.

See also

• Extranatural transformation
• Natural transformation

External links

• dinatural transformation at the nLab