From 2b830cb2d9c2237fcb7809bab7c64966098ea6fb Mon Sep 17 00:00:00 2001
From: Franciszek Malinka <franciszek.malinka@gmail.com>
Date: Sun, 17 Jul 2022 14:16:41 +0200
Subject: Oby ostatnie poprawki

---
 sections/fraisse_classes.tex | 11 ++++++++---
 1 file changed, 8 insertions(+), 3 deletions(-)

(limited to 'sections/fraisse_classes.tex')

diff --git a/sections/fraisse_classes.tex b/sections/fraisse_classes.tex
index 87647c6..1126dee 100644
--- a/sections/fraisse_classes.tex
+++ b/sections/fraisse_classes.tex
@@ -283,13 +283,14 @@
 	  \end{tikzcd}
 	\end{center}
 
+	and $A\sqcup_C B\in\cC$.
 	$A\sqcup_C B$ here is an $L$-structure with domain $A\cup B$ such that
 	for every $n$-ary symbol $R$ from $L$, $n$-tuple $\bar{a}\subseteq A\cup B$,
-	we have that $A\sqcup B\models R(\bar{a})$ if and only if [$\bar{a}\subseteq A$ and
+	we have that $A\sqcup_C B\models R(\bar{a})$ if and only if [$\bar{a}\subseteq A$ and
 	$A\models R(\bar{a})$] or [$\bar{a}\subseteq B$ and $B\models R(\bar{a})$].
   \end{definition}
 
-  Actually we did already implicitly worked with free amalgamation in the 
+  Actually we did already implicitly work with free amalgamation in the 
   Proposition \ref{proposition:finite-graphs-fraisse-class}, showing that
   the class of finite graphs is indeed a Fraïssé class.
 
@@ -298,7 +299,7 @@
   Recall, $\Cospan(\cC)$, $\Pushout(\cC)$ are the categories of cospan
   and pushout diagrams of the category $\cC$. We have also denoted the notion
   of cospans and pushouts with a fixed base structure $C$ denoted
-  as $\Cospan_C(\cC)$ and $Pushout_C(\cC)$.
+  as $\Cospan_C(\cC)$ and $\Pushout_C(\cC)$.
 
   \begin{definition}
 	\label{definition:canonical_amalgamation}
@@ -346,6 +347,10 @@
 	\end{itemize}
   \end{definition}
 
+  \begin{remark}
+	Free amalgamation is canonical.
+  \end{remark}
+
   From now on in the paper, when $A$ is an $L$-structure and $\alpha$ is 
   an automorphism of
   $A$, then by $(A, \alpha)$ we mean the structure $A$ expanded by the
-- 
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