# The Stacks Project

## Tag 041Y

Lemma 65.10.15. The property $\mathcal{P}(f) =$''$f$ is an isomorphism'' is fpqc local on the base.

Proof. Combine Lemmas 65.10.6 and 65.10.14. $\square$

The code snippet corresponding to this tag is a part of the file spaces-descent.tex and is located in lines 1391–1395 (see updates for more information).

\begin{lemma}
\label{lemma-descending-property-isomorphism}
The property $\mathcal{P}(f) =$$f$ is an isomorphism''
is fpqc local on the base.
\end{lemma}

\begin{proof}
Combine Lemmas \ref{lemma-descending-property-surjective}
and \ref{lemma-descending-property-open-immersion}.
\end{proof}

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