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Tag 0CLH

Chapter 86: Morphisms of Algebraic Stacks > Section 86.33: Valuative criteria

Lemma 86.33.7. The base change of a morphism of algebraic stacks which satisfies the uniqueness part of the valuative criterion by any morphism of algebraic stacks is a morphism of algebraic stacks which satisfies the uniqueness part of the valuative criterion.

Proof. Follows from Lemma 86.33.4 and the definition. $\square$

    The code snippet corresponding to this tag is a part of the file stacks-morphisms.tex and is located in lines 7576–7582 (see updates for more information).

    \begin{lemma}
    \label{lemma-base-change-uniqueness}
    The base change of a morphism of algebraic stacks which satisfies the
    uniqueness part of the valuative criterion by any morphism of
    algebraic stacks is a morphism of algebraic stacks which satisfies the
    uniqueness part of the valuative criterion.
    \end{lemma}
    
    \begin{proof}
    Follows from Lemma \ref{lemma-cat-dotted-arrows-base-change}
    and the definition.
    \end{proof}

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