ar X iv : 0 70 9 . 14 21 v 9 [ m at h . L O ] 1 0 O ct 2 00 7 Coherence in Linear Predicate Logic

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 of [7] and [8], 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. Mathematics Subject Classification (2000): 03F52, 03F05, 03F07, 18D10, 18D15, 18C05, 18A15