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Tag 0CLM

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

Lemma 86.33.12. The composition of morphisms of algebraic stacks which satisfy the existence part of the valuative criterion is another morphism of algebraic stacks which satisfies the existence part of the valuative criterion.

Proof. Follows from Lemma 86.33.5 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 7690–7696 (see updates for more information).

    \begin{lemma}
    \label{lemma-composition-existence}
    The composition of morphisms of algebraic stacks which satisfy the
    existence part of the valuative criterion is another
    morphism of algebraic stacks which satisfies the
    existence part of the valuative criterion.
    \end{lemma}
    
    \begin{proof}
    Follows from Lemma \ref{lemma-cat-dotted-arrows-composition}
    and the definition.
    \end{proof}

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