Let \(P, Q: \mathcal {C}^{\mathsf {op}} × \mathcal {C} \to \mathcal {D}\) be functors.
A family of morphisms \(\alpha _u : P(u,u) \to Q(u,u)\) is dinatural in \(u\) if the following hexagon commutes for every \(f : u \to u'\) in \(\mathcal {C}\).
\[ \begin {array}{ccccccc} & & P(u,u) & \overset {\alpha _{u}}{\to } & Q(u,u)\\ & \overset {\mathclap {P(f,u)}}{\nearrow } & & & & \overset {\mathclap {Q(u,f)}}{\searrow }\\ P(u',u) & & & & & & Q(u,u')\\ & \underset {\mathclap {P(u',f)}}{\searrow } & & & & \underset {\mathclap {Q(f,u')}}{\nearrow }\\ & & P(u',u') & \underset {\alpha _{u'}}{\to } & Q(u',u') \end {array} \]