  To provide a categorical semantics for co-intuitionistic logic one has to
face the fact, noted by Tristan Crolard, that the definition of co-exponents as
adjuncts of coproducts does not work in the category Set, where coproducts are
disjoint unions. Following the familiar construction of models of
intuitionistic linear logic with exponential"!", we build models of
co-intuitionistic logic in symmetric monoidal left-closed categories with
additional structure, using a variant of Crolard's term assignment to
co-intuitionistic logic in the construction of a free category.
