Gavin Bierman wrote a very clear paper "What is a Categorical Model of Intuitionistic Linear Logic?" in 1995. Andrea Schalk has some detailed notes on her web page "What is a Categorical Model of Linear Logic?" Paul-Andre Mellies has two versions "Categorical models of linear logic revisited" (2003) and "Categorical Semantics of Linear Logic" (2012). Together with Milly Maietti, Paola Maneggia and Eike Ritter, I have Relating Categorical Semantics for Intuitionistic Linear Logic. By myself I have Categorical Semantics of Linear Logic for
All, which needs some cleaning up and updating in places. Why do we need so many? Need to write a post with preliminary conclusions.
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