Proposition 10

Let X and Y be topological spaces and let $f$ be a continuous mapping of X into Y. Suppose that the space X is simply connected, that the space $X\times_YX$ is locally arcwise connected, and that every descent datum relative to $f$ on a covering of X is effective and the quotient space is a covering of Y. Then the groupoid morphism $\varpi '(f)$ of Coeg($f$) into $\varpi (Y)$ is injective.

Under the hypotheses of the proposition, $f$ is strict ( IV, p. 394, remark); moreover, one may suppose that it is surjective.