The Stacks project

Situation 70.6.1. Let $S$ be a scheme. Let $B = \mathop{\mathrm{lim}}\nolimits B_ i$ be a limit of a directed inverse system of algebraic spaces over $S$ with affine transition morphisms (Lemma 70.4.1). Let $0 \in I$ and let $f_0 : X_0 \to Y_0$ be a morphism of algebraic spaces over $B_0$. Assume $B_0$, $X_0$, $Y_0$ are quasi-compact and quasi-separated. Let $f_ i : X_ i \to Y_ i$ be the base change of $f_0$ to $B_ i$ and let $f : X \to Y$ be the base change of $f_0$ to $B$.