  Diagram chasing is not an easy task. The coherence holds in a generalized
sense if we have a mechanical method to judge whether given two morphisms are
equal to each other. A simple way to this end is to reform a concerned category
into a calculus, where the instructions for the diagram chasing are given in
the form of rewriting rules. We apply this idea to the categorical semantics of
the linear logic. We build a calculus directly on the free category of the
semantics. It enables us to perform diagram chasing as essentially one-way
computations led by the rewriting rules. We verify the weak termination
property of this calculus. This gives the first step towards the mechanization
of diagram chasing.
