  Using the set-up of deformation categories of Talpo and Vistoli, we
re-interpret and generalize, in the context of cartesian morphisms in abstract
categories, some results of Rim concerning obstructions against extensions of
group actions in infinitesimal deformations. Furthermore, we observe that
finite \'etale coverings can be infinitesimally extended and the resulting
formal scheme is algebraizable. Finally, we show that pre-Tango structures
survive under pullbacks with respect to finite, generically \'etale surjections
$\pi:X\rightarrow Y$, and record some consequences regarding Kodaira vanishing
in degree one.
