@TECHREPORT{Schalk04whatsis, author = {Andrea Schalk}, title = {Whats is a categorical model of linear logic}, institution = {}, year = {2004} }

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Abstract

The aim of these notes is to give an outline of the categorical structure required for a model of linear logic. That means that we only try to motivate the various conditions imposed on such models; this is by no means intended to be a full account. For intuitionistic linear logic a detailed description of the process of defining such a model can be found in Gavin Bierman’s thesis [Bie94]. There are a number of exercises in these notes, they either aim to give examples for the various notions defined or they state minor results that are used subsequently and which hopefully are not too difficult to establish. If the category theory in these notes is too advanced you may want to try [BS] which does not assume any knowledge in that area at all, but proceeds fairly rapidly to the notions we use here. Originally these notes were written for my PhD students, but since I made the first version available on my webpage a number of people have told me they found them useful. As a result I felt obliged to to add details which were rather sketchy in the original account. In particular the account now contains more proofs and so I am hopeful that the various formulations of the notion of linear exponential comonad are finally correct. I would like to thank Paola Maneggia, Peter Selinger, Robin Houston and Nicola Gambino for useful feedback on these