Exercise 1, § 4

Let $X$ and $Y$ be topological spaces and let $f: X\rightarrow Y$ be a continuous mapping. Let $(T, p)$ be a $Y$-space. The canonical descent datum $\tau$ on the $X$-space $Z = X\times_YT$ is effective (IV, p. 385, prop. 1), the canonical mapping $Z/R_{\tau}\rightarrow T$ is injective and continuous. It is nevertheless not necessarily surjective, nor strict.