On categorical semantics for the exponential modality in linear logic:
Nick Benton, Gavin Bierman, Valeria de Paiva, Martin Hyland, Linear -Calculus and Categorical Models Revisited, in Computer Science Logic. CSL 1992, Lecture Notes in Computer Science 702, Springer (1993) [doi:10.1007/3-540-56992-8_6]
Gavin Bierman, On Intuitionistic Linear Logic, Cambridge (1993) [pdf]
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