Lemma 87.15.4 (0CB9)—The Stacks project

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Table of contents
Part 5: Topics in Geometry
Chapter 87: Formal Algebraic Spaces
Section 87.15: Fibre products
Lemma 87.15.4 (cite)

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Lemma 87.15.4. Let $S$ be a scheme. Let $X \to Z$ and $Y \to Z$ be morphisms of formal algebraic spaces over $S$ . Then $(X \times _ Z Y)_{red} = (X_{red} \times _{Z_{red}} Y_{red})_{red}$ .

Proof. This follows from the universal property of the reduction in Lemma 87.12.1. $\square$

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