Lemma 92.10.2. Let $S$ be an object of $\mathit{Sch}_{fppf}$. Let $\mathcal{P}$ be as in Definition 92.10.1. Consider a $2$-commutative diagram

of $1$-morphisms of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. Assume the horizontal arrows are equivalences and $f$ (or equivalently $f'$) is representably by algebraic spaces. Then $f$ has $\mathcal{P}$ if and only if $f'$ has $\mathcal{P}$.

## Comments (2)

Comment #26 by David Zureick-Brown on

Comment #5939 by Dario Weißmann on