  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. Our results
delve into the differentiability of cotranslations, along with dimension
invariance and diagonalization, utilizing a generalized notion of kinematic
similarity.
