Puzzle 161:

Preservation of identities follows easily from,

\\[
\mathrm{hom}(id\_c , id\_{c'})(f) = id\_{c'} \circ f \circ id_c
\\],

and the preservation of the composite \\(j\circ k \circ l\\) is given by,
\\[\begin{align}
\mathrm{hom}(f,g)(j\circ k \circ l) \\\\
=\mathrm{hom}(f,g)\circ \mathrm{hom}(l,j)(k) \\\\
= g\circ j\circ k \circ l \circ f.
\end{align}
\\]