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In category theory, a dinatural transformation <math>\alpha</math> between two functors

<math>S,T : \mathrm{C}^{\mathrm{op}}\times\mathrm{C}\to\mathrm{X}</math>,

written

<math>\alpha : S\ddot\to T</math>,

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

<math>\alpha_c : S(c,c)\to T(c,c)</math> of X

and satisfies the following coherence property: for every morphism <math>f:c\to c’</math> of C the diagram

commutes.