The following is taken from: $\textit{Partial Differential Control Theory Vol 1: Mathematical tools}$ by J F. Pommaret
$\color{Green}{Background:}$
$\textbf{Proposition 1.59.}$ Let
$$0\to M'\xrightarrow{f}M\xrightarrow{g}M''\to 0$$
be a short exact sequence of $A-$modules.
$(i)$ If $M'$ and $M''$ are finitely generated, then $M$ is also finitely generated.
$(ii)$ If $M$ is finitely presented and $M'$ is finitely generated, then $M''$ is also finitely presented.
$\textit{Proof.}$ We have the following commutative and exact diagram:
The left vertical column is a finite presentation of $M$ where $F$ is a free module and $K$ is finitely generated. The kernel $L$ of the composition $F\to M\to M''$ is containing $K$ as a submodule and by chasing we obtain an isomorphism $M'\equiv L/K.$ Accordingly, $L/K$ is finitely generated and $L$ is finitely generated too because of $i$). It follows that $M''$ is finitely presented.
$\color{Red}{Questions:}$
In the proof above for part $(ii)$ of Proposition 1.59,
the notation:
I would like to know what it means in the context of the commutative diagram.
Thank you in advance
It stands for $F \xrightarrow{id_F} F$.