Lemma 70.4.2. Let S be a scheme. Let I be a directed set. Let (X_ i, f_{ii'}) be an inverse system over I of algebraic spaces over S with affine transition maps. Let X = \mathop{\mathrm{lim}}\nolimits _ i X_ i. Let 0 \in I. Suppose that T \to X_0 is a morphism of algebraic spaces. Then
T \times _{X_0} X = \mathop{\mathrm{lim}}\nolimits _{i \geq 0} T \times _{X_0} X_ i
as algebraic spaces over S.
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