@@ -1120,7 +1120,10 @@ We now turn to truncations of chain complexes.

\end{itemize}

\end{proposition}

\begin{proof}

This is a typical example of a transfer of a cofibrantly generated model structure along a right adjoint as in \cite[Proposition 2.3]{beke2001sheafifiableII}. The only \emph{a priori} non-trivial hypothesis to check is that there exists a set $J$ of generating trivial cofibrations of the projective model structure on $\Ch$ such that for every $j \colon A \to B$ in $J$ and every cocartesian square

This is a typical example of a transfer of a cofibrantly generated model

structure along a right adjoint as in \cite[Proposition

2.3]{beke2001sheafifiableII}. Since the weak equivalences of the projective model

structure on $\Ch$ are closed under filtered colimits \cite[Theorem 2.6.15]{weibel1995introduction}, the only \emph{a priori} non-trivial hypothesis to check is that there exists a set $J$ of generating trivial cofibrations of the projective model structure on $\Ch$ such that for every $j \colon A \to B$ in $J$ and every cocartesian square

\[

\begin{tikzcd}

\tau^{i}_{\leq n}(A)\ar[r]\ar[d,"\tau^{i}_{\leq n}(j)"']& X \ar[d,"g"]\\