Let $A^\bullet$ be the complex:
$\cdots \rightarrow A^{n-2} \xrightarrow{d^{n-2}} A^{n-1} \xrightarrow{d^{n-1}} A^{n} \xrightarrow{d^{n}} A^{n+1} \xrightarrow{d^{n+1}} A^{n+2} \xrightarrow{d^{n+2}} \cdots$,
consider the truncation $\tau_{\leq n}A^{\bullet}$:
$\cdots \rightarrow A^{n-2} \xrightarrow{d^{n-2}} A^{n-1} \xrightarrow{d^{n-1}} \ker d^{n} \rightarrow 0 \rightarrow 0 \rightarrow \cdots$,
consider a resolution for $\tau_{\leq n}A^{\bullet}$: the quasi-isomorphism $f_n: P^{\bullet}_{n} \rightarrow \tau_{\leq n}A^{\bullet}$
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Now I'm reading a paper and I got to this part that says:
"... let $g: P^{\bullet}_{n} \rightarrow \tau_{\leq n + 1}A^{\bullet}$ be the chain map induced by $f_n$...".
But I wanted to be perfectly clear and ask, what is this chain map $g$? Is it
If so, what would be the map $q$?
