Dinatural transformation; w </math>
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.