On categorical semantics for the exponential modality in linear logic:
Nick Benton, Gavin Bierman, Valeria de Paiva, Term assignment for intuitionistic linear logic, Technical report 262, Computer Laboratory, University of Cambridge (August 1992) [pdf, pdf]
(published abridged as BBPH92)
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]
and specifically as the comonad induced from an adjunction between ordinary types and linear types:
On modal operator-like monads in computer science:
On monads in computer science:
Nick Benton, John Hughes, Eugenio Moggi, Monads and Effects, in: Applied Semantics, Lecture Notes in Computer Science 2395, Springer (2002) 42-122 [doi:10.1007/3-540-45699-6_2]
Nick Benton, Categorical Monads and Computer Programming, in: Impact150: stories of the impact of mathematics. London Mathematical Society (2015) [pdf, pdf, doi:10.1112/i150lms/t.0002]
On dependent linear type theory:
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