Question about slice category from Allufi chapter 0

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I have a quick question maybe there is something trivial confusing me. So, here I don't know why we have $f_1$ and $f_2$ the way they are. Shouldn't $f_1 : Z_2 \rightarrow A$ and $f_2 : Z_1 \rightarrow A$. Because, then we will have that $\sigma : f_1 \rightarrow f_2$ defined as $\sigma \ f_1 = f_1 \sigma = f_2$ enter image description here