Dinatural transformation

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

S,T:C^{{{\mathrm {op}}}}\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 $f:c\to c'$ of C the diagram

commutes.

The composition of two dinatural transformations need not be dinatural.

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