If we set the first variable of \\(\mathrm{hom}\\) to \\(id_{source(h)}\\), then I think our double-ended queue gets turned into something like a linked list,

\\[
\mathrm{hom}(id_{source(h)}, k)\cdots\mathrm{hom}(id_{source(h)}, g)(h) \\\\
= k \circ \cdots \circ g \circ h \circ id_{source(h)} \circ \cdots \circ id_{source(h)}
\\]

where \\(id_{source(h)}\\) acts like the list's \\(\texttt{null}\\) element.