In an short exact sequences, like the one appear in the indentation and the one appear in the included screenshot:
$\{0\}\stackrel{\rm f_{i-1}}{\longrightarrow}A\stackrel{\rm f_{i}}{\longrightarrow}B\stackrel{\rm f_{i+1}}{\longrightarrow}C\stackrel{\rm f_{i+2}}{\longrightarrow}\{0\}$
where $\text{Im }f_{i-1} = \text{Ker }f_{i}$.
I understand why the $f_{i+1}$ map is a surjective map, since $\text{Ker}f_{i+1}=C$. But according to here, $\pi$, $\iota$ in place of $f_{i+1}$, $f_{i}$ respectively and change of letters designating the sets being map to. Section 1.11 second paragraph pg 79, also included in the screenshot also calls it a projection map. Can someone explain to me in what sense it is a projection map.
Thank you in advance