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.