  We formulate an elementary condition on an involutive quantaloid Q under
which there is a distributive law from the Cauchy completion monad over the
symmetrisation comonad on the category of Q-enriched categories. For such
quantaloids, which we call Cauchy-bilateral quantaloids, it follows that the
Cauchy completion of any symmetric Q-enriched category is again symmetric.
Examples include Lawvere's quantale of non-negative real numbers and Walters'
small quantaloids of closed cribles.
