From 1cdc392e139bf3b487a8ed3667aeabe844d4ea1d Mon Sep 17 00:00:00 2001 From: Aise Johan de Jong Date: Fri, 30 Apr 2021 20:08:38 -0700 Subject: [PATCH] Add an internal reference to a proof Thanks to Dario Weissmann https://stacks.math.columbia.edu/tag/049W#comment-5972 --- groupoids-quotients.tex | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/groupoids-quotients.tex b/groupoids-quotients.tex index 94cc817b6..c978cfcec 100644 --- a/groupoids-quotients.tex +++ b/groupoids-quotients.tex @@ -389,7 +389,8 @@ \section{Categorical quotients} \begin{proof} Let $X_{red}$ be the reduction of the algebraic space $X$. Since $U$ is reduced the morphism $\phi : U \to X$ factors through -$i : X_{red} \to X$ (insert future reference here). Denote this morphism +$i : X_{red} \to X$ (Properties of Spaces, Lemma +\ref{spaces-properties-lemma-map-into-reduction}). Denote this morphism by $\phi_{red} : U \to X_{red}$. Since $\phi \circ s = \phi \circ t$ we see that also $\phi_{red} \circ s = \phi_{red} \circ t$ (as $i : X_{red} \to X$ is a monomorphism). Hence by the universal property