  Coherence with respect to Kelly-Mac Lane graphs is proved for categories that
correspond to the multiplicative fragment without constant propositions of
classical linear first-order predicate logic without or with mix. To obtain
this result, coherence is first established for categories that correspond to
the multiplicative conjunction-disjunction fragment with first-order
quantifiers of classical linear logic, a fragment lacking negation. These
results extend results published in previous two books by the authors, where
coherence was established for categories of the corresponding fragments of
propositional classical linear logic, which are related to proof nets, and
which could be described as star-autonomous categories without unit objects.
