Natural transformation of multifunctors [mde-DCTG]

For \(F,G : M \to N\) multifunctors, a natural transformation \(\alpha : F \to G\) is a collection of unary maps \(\{\alpha _X : [FX] \to GX\}_{X \in M}\) in \(N\) such that for every \(f : X_1 ... X_n \to X\) in \(M\), \[Ff \mathbin {⨟} \alpha _X = (\alpha _{X_1}, ... \alpha _{X_n}) ; Gf.\]