My PhD thesis (2007) was available for several years from my web site at the University of Manchester, but since that site was taken down it’s been unavailable. Today’s announcement is that I’ve finally got round to uploading it to GitHub.
I’ve also submitted it to the arXiv, where it is now available.
I think this extract from the introduction goes some way to conveying the flavour of the thing, i.e. that the overall approach is pretty abstract even by the standards of abstract mathematics, let alone computer science.
In fact there is nothing particularly special about promonoidal categories in an abstract sense. They are but one example of the general notion of pseudomonoid in a monoidal bicategory, and we expect (and shall prove) that much of what is known about monoidal categories in particular is actually true of pseudomonoids in general, when formulated appropriately. Furthermore, when considering structures internal to a monoidal bicategory there is nothing particularly special about pseudomonoids! The translation procedure can in fact be carried through for a substantial class of structures internal to a monoidal bicategory.
But there are some more concrete descriptions near the end, and if you should happen to be interested in models of multiplicative linear logic without units – admittedly a fairly niche topic – then I reckon it’s worth a look, even if I do say so myself.
It looks like I used to be a pretty ninja TeX programmer, as well!