Fix mistake with matrices in Schanuel's lemma

Thanks to Matthé van der Lee https://stacks.math.columbia.edu/tag/00O3#comment-4019
stacks · Apr 6, 2019 · d56ebdf · d56ebdf
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diff --git a/CONTRIBUTORS b/CONTRIBUTORS
@@ -295,6 +295,7 @@ Burt Totaro
 Ravi Vakil
 Michel Van den Bergh
 Theo van den Bogaart
+Matthé van der Lee
 Jeroen van der Meer
 Remy van Dobben de Bruyn
 Kevin Ventullo

diff --git a/algebra.tex b/algebra.tex
@@ -25431,12 +25431,12 @@ \section{Rings of finite global dimension}
 \xymatrix{
 0 \ar[r] &
 K \oplus P_2 \ar[r]_{(c_1, \text{id})} \ar[d] &
-P_1 \oplus P_2 \ar[r]_{(0, p_2)} \ar[d] &
+P_1 \oplus P_2 \ar[r]_{(p_1, 0)} \ar[d] &
 M \ar[r] \ar@{=}[d] &
 0 \\
 0 \ar[r] &
 P_1 \oplus L \ar[r]^{(\text{id}, c_2)} &
-P_1 \oplus P_2 \ar[r]^{(p_1, 0)} &
+P_1 \oplus P_2 \ar[r]^{(0, p_2)} &
 M \ar[r] &
 0
 }
@@ -25463,18 +25463,18 @@ \section{Rings of finite global dimension}
 \xymatrix{
 0 \ar[r] &
 K \oplus P_2 \ar[r]_{(c_1, \text{id})} &
-P_1 \oplus P_2 \ar[r]_{(0, p_2)} &
+P_1 \oplus P_2 \ar[r]_{(p_1, 0)} &
 M \ar[r] &
 0 \\
 0 \ar[r] &
 N \ar[r] \ar[d] \ar[u] &
 P_1 \oplus P_2 \ar[r]_{(p_1, p_2)}
-\ar[d]_T \ar[u]^S &
+\ar[d]_S \ar[u]^T &
 M \ar[r] \ar@{=}[d] \ar@{=}[u] &
 0 \\
 0 \ar[r] &
 P_1 \oplus L \ar[r]^{(\text{id}, c_2)} &
-P_1 \oplus P_2 \ar[r]^{(p_1, 0)} &
+P_1 \oplus P_2 \ar[r]^{(0, p_2)} &
 M \ar[r] &
 0
 }