  Braided monoidal categories arise naturally as centres of monoidal categories
and have been the focus of much recent attention in both mathematics and
physics. By suitably restricting the use of the exchange rule, we obtain a
sequent calculus whose categorical semantics may be seen as freely constructing
the centre of a monoidal category. This calculus is shown to admit a strongly
normalising and confluent cut elimination procedure. The resulting logic fits
neatly into the landscape of noncommutative logics and is distinguished by
possessing a particularly perspicuous semantics.
