Several investigations have alreadyshown that the presence of higher-order interactions maysignificantly impact the dynamics on networked systems,from diffusion [ 29, 30] and synchronization [31 , 32 ] tosocial [ 33– 35 ] and evolutionary processes [36 ], possiblyleading to the emergence of abrupt (explosive) transitionsbetween states. And although most research in complexsystems focuses on the dynamical evolution of the statesof the nodes, it is natural to consider that higher-orderstructures (described by hyperedges) could themselvespossess a dynamical state, leading to a whole newpanorama of dynamical processes.