  Synchronization has received a lot of attention from the scientific community
for systems evolving on static networks or higher-order structures, such as
hypergraphs and simplicial complexes. In many relevant real world applications,
the latter are not static but do evolve in time, in this paper we thus discuss
the impact of the time-varying nature of high-order structures in the emergence
of global synchronization.
  To achieve this goal we extend the master stability formalism to account, in
a general way, for the additional contributions arising from the time evolution
of the higher-order structure supporting the dynamical systems. The theory is
successfully challenged against two illustrative examples, the Stuart-Landau
nonlinear oscillator and the Lorenz chaotic oscillator.
