diff --git a/.gitmodules b/.gitmodules
index 1197bac..d9a7d79 100644
--- a/.gitmodules
+++ b/.gitmodules
@@ -1,3 +1,3 @@
 [submodule "LatexPackagesBuild"]
 	path = LatexPackagesBuild
-	url = https://gitlab.com/latexci/packages/LatexPackagesBuild.git
+    url = https://git.abstractnonsen.se/latex/latex-packages-build
diff --git a/inputs/lecture_23.tex b/inputs/lecture_23.tex
index 6068d5d..fde2837 100644
--- a/inputs/lecture_23.tex
+++ b/inputs/lecture_23.tex
@@ -160,14 +160,14 @@ Let $I$ be a linear order
             we have that $F_\gamma = \bigcap_{\alpha < \gamma} F_\alpha$,
             since $(X_\gamma,\Z)$ is the inverse limit of
             $\{(X_{\alpha}, \Z):\alpha < \gamma\}$.
-        \item For all $\alpha < \beta$, $F_{\alpha+1} \subsetneq F_\alpha$,
+        \item For all $\alpha$ it is $F_{\alpha+1} \subsetneq F_\alpha$,
             because $\pi^{\alpha+1}_\alpha \colon (X_{\alpha+1},\Z) \to (X_\alpha,\Z)$
             is not a bijection
             and all the fibers are isomorphic.
     \end{itemize}
 
     So $(F_\alpha)_{\alpha \le \beta}$ is a strictly
-    increasing chain of closed subsets.
+    decreasing chain of closed subsets.
     But $X$ is second countable,
     so $\beta$ is countable:
     Let $\{U_n\} = \cB$ be a countable basis