sitemati typo

2026-05-19 15:27:49 +02:00
parent df9a3121d5
commit ae0cde5c65
4 changed files with 4 additions and 4 deletions
@@ -96,7 +96,7 @@
 		
 		
 		\begin{theorem}\label{completenesscomma}
-			Let $\mathcal{A}$ and $\mathcal{B}$ be two finitely cocomplete categories and let $F:\mathcal{A} \to \mathcal{C}$, $\mathcal{B} \to \mathcal{C}$ two functors. If $F$ is a continuous functor - i.e. preserves small colimits - then the comma category $(F\downarrow G)$ is finitely cocomplete; moreover the forgetful functors are continuous. \\
+			Let $\mathcal{A}$ and $\mathcal{B}$ be two finitely cocomplete categories and let $F:\mathcal{A} \to \mathcal{C}$, $\mathcal{B} \to \mathcal{C}$ two functors. If $F$ is a cocontinuous functor - i.e. preserves small colimits - then the comma category $(F\downarrow G)$ is finitely cocomplete; moreover the forgetful functors are continuous. \\
 			Analogously if $\mathcal{A}$ and $\mathcal{B}$ are finitely complete categories and $G: \mathcal{A} \to \mathcal{C}$ is continuos - i.e. preserves small limits - then $(F \downarrow G)$ is finitely complete and both forgetful functors are continuos. 
 			
 		\end{theorem}