Fix a second proof in algebra

Thanks to Shota Inoue
https://stacks.math.columbia.edu/tag/00DD#comment-5989

CONTRIBUTORS

@@ -179,6 +179,7 @@ John Hosack
 Xiaowen Hu
 Yuhao Huang
 Yu-Liang Huang
+Shota Inoue
 Ariyan Javanpeykar
 Lena Min Ji
 Qingyuan Jiang

algebra.tex

@@ -1949,8 +1949,9 @@ \section{Tensor products}
 Categories, Lemma \ref{categories-lemma-adjoint-exact}.
 
 \medskip\noindent
-Second direct proof. Let $P = \colim (M_i \otimes N)$, $M = \colim M_i$.
-Then for all $i\leq j$, the following diagram commutes:
+Second direct proof. Let $P = \colim (M_i \otimes N)$ with coprojections
+$\lambda_i : M_i \otimes N \to P$. Let $M = \colim M_i$ with coprojections
+$\mu_i : M_i \to M$. Then for all $i\leq j$, the following diagram commutes:
 $$
 \xymatrix{
 M_i \otimes N \ar[r]_{\mu_i \otimes 1} \ar[d]_{\mu_{ij} \otimes 1} &
@@ -1959,10 +1960,9 @@ \section{Tensor products}
 M \otimes N
 }
 $$
-By Lemma \ref{lemma-homomorphism-limit},
-these maps induce a unique homomorphism
-$\psi : P \to M \otimes N$, with $\lambda_i : M_i \otimes N \to P$ given by
-$\lambda_i = \pi \circ (\iota_i \otimes 1)$.
+By Lemma \ref{lemma-homomorphism-limit} these maps induce a unique homomorphism
+$\psi : P \to M \otimes N$ such that
+$\lambda_i = \psi \circ (\mu_i \otimes 1)$.
 
 \medskip\noindent
 To construct the inverse map, for each $i\in I$, there is the canonical