<p>We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific kind of groupoid morphism, and establish a correspondence between cotranslations and skew-products. We give applications of cotranslations to nonautonomous equations, both in differences and differential. We also give several other examples on different groups. Our results delve into the differentiability of cotranslations, along with dimension invariance and diagonalization, utilizing a generalized notion of kinematic similarity.</p>