There isn't very much here right now, but hopefully the collection will grow over time. I would be delighted to receive feedback on any of the items below. That would allow me to revise these notes.
Introduction to Games used for Semantics. This is a gentler introduction to the topic than most others I have seen, and consequently it doesn't get to any real applications. The simplest category of games as a model of linear logic is described here, and an appendix gives the precise definition of such a model. It is suitable for readers who have had some exposure to category theory. There are typos in there, and I think it's due a revamp. But that will only happen if I can see some evidence that anybody's reading it. There is also a pdf version.
Some notes on monads. This is a short introduction to monads. It motivates the definition, makes the connection to Kleisli triples and then proceeds to explain the Kleisli category and the category of Eilenberg Moore algebras for a monad. It assumes that the reader is familiar with category theory up to adjunctions. Again there is a pdf version.
What is a categorical model of linear logic?. This is an introduction to what it means to be categorical model of linear logic. While it tries not to assume more than the definition of adjunction, it gets somewhat dense when it comes to giving the interpretation of the linear exponentials. Not all diagrams are given explicitly. However, a characterization for such a model is given which does not not seem to be present in the literature. There is also a pdf version.
Together with
Martin Hyland I've written a paper on the
(double) glueing technique, and how it can be used to build more
sophisticated models of linear logic from simple ones. This includes
a description of using a notion of