Global Actions

A global action is an algebraic analogue of a topological space. It consists of group actions $G_{\alpha }\curvearrowright X_{\alpha }$, $(\alpha \in \mathrm{\Phi })$, which fulfill a certain compatibility condition. We investigate the homotopy theory of global actions. The main result establishes a Galois type correspondence between connected coverings of a given connected global action and subgroups of the fundamental group of that action.