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]
Gavin Bierman, On Intuitionistic Linear Logic, Cambridge (1994) [pdf, pdf]
A natural deduction-formulation of modal logic (S4/S5) and making explicit the necessity modal operator as a comonad:
Gavin M. Bierman, Valeria de Paiva, Intuitionistic necessity revisited, School of Computer Science research reports-University of Birmingham CSR (1996) [researchgate, pdf]
Gavin M. Bierman, Valeria de Paiva, On an Intuitionistic Modal Logic Studia Logica 65 (2000) 383–416 [https://doi.org/10.1023/A:1005291931660, pdf]
see also:
Introducing polymonads:
Nataliya Guts, Michael Hicks, Nikhil Swamy, Daan Leijen, Gavin Bierman, Polymonads, Extended version of POPL’13 submission [pdf, pdf]
Michael Hicks, Gavin Bierman, Nataliya Guts, Daan Leijen, Nikhil Swamy, Polymonadic Programming, EPTCS 153 79-99 (2014) [arXiv:1406.2060, doi:10.4204/EPTCS.153.7]
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