The Stacks project

Lemma 88.23.7. In the situation above. If $f$ is (quasi-)separated, then $f_{/T}$ is too.

Proof. (Separation conditions on morphisms of formal algebraic spaces are discussed in Formal Spaces, Section 87.30.) We have to show that if $\Delta _ f$ is quasi-compact, resp. a closed immersion, then the same is true for $\Delta _{f_{/T}}$. This follows from the discussion in Remark 88.23.6 and Lemmas 88.23.5 and 88.23.3. $\square$

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