Remark 2

Let B be an unloopable space; every operation of the groupoid $\varpi (B)$ on a B-space is without local monodromy (cf. III, p. 313, remark). In particular, in order that a mapping $p: E\rightarrow B$ make E into a covering of B, it is necessary and sufficient that it be étale, separated and that it satisfy the path lifting property (III, p. 315, corollary 3).