  Eklund et al. (2002) present a graphical technique aimed at simplifying the
verification of various category-theoretic constructions, notably the
composition of monads. In this note we take a different approach involving
string rewriting. We show that a given tuple $(T,\mu,\eta)$ is a monad if and
only if $T$ is a terminal object in a certain category of strings and rewrite
rules, and that this fact can be established by proving confluence of the
rewrite system. We illustrate the technique on the monad composition problem.
We also give a characterization of adjunctions in terms of rewrite categories.
