Triangle identities as string diagrams

Question

From Remark 2.2.9:

How exactly do these diagrams translate to these triangle identities?

E.g. the first triangle identity has $F\eta$ and $\epsilon F$ in it; how to see them and their composition in the diagram?

Answer 1

$F \eta$ is the top half of the first diagram, $\varepsilon F$ is the bottom half, and the composition is given by sticking the top half to the bottom half (note that if you cut the diagram in half it intersects the bottom $F$ line, then $G$, then the top $F$ line; this corresponds to the $FGF$ portion of the first triangle identity.

This is not quite the best way of drawing string diagrams for the triangle identities; ideally it should be clearer that functors correspond to line segments.

Answer 2

To complement Qiaochu's description with an illustration from Wikipedia:

Tom Leinster did mention how $1: F \Rightarrow F$ is drawn as a simple string without circles and how horizontal composition is depicted right before, but I agree with you and Qiaochu that the diagrams in the book is not clear.