  The left and right diameters of a monoid are topological invariants defined
in terms of suprema of lengths of derivation sequences with respect to finite
generating sets for the universal left or right congruences. We compute these
parameters for the endomorphism monoid $End(C)$ of a chain $C$. Specifically,
if $C$ is infinite then the left diameter of $End(C)$ is 2, while the right
diameter is either 2 or 3, with the latter equal to 2 precisely when $C$ is a
quotient of $C{\setminus}\{z\}$ for some endpoint $z$. If $C$ is finite then so
is $End(C),$ in which case the left and right diameters are 1 (if $C$ is
non-trivial) or 0.
