Morphism colored operads

Definition 12.2.2. If \(\Pp \) is another colored operad, then a morphism \(f \colon \Oo \to \Pp \) of colored operads consists of a map of sets \(f\colon \Oo ^{\simeq } \to \Pp ^{\simeq }\) on colors and for all colors \(x,y_1,\dots ,y_n \in \Oo ^{\simeq }\) a map \[ f\colon \Oo ((y_1,\dots ,y_n);x) \to \Pp ((fy_1,\dots ,fy_n);fx) \] on multimorphisms, in such a way that \(f\) preserves identity operations, composition of operations and permutations.