Uses of “Categories for Types”

This text is intended to be a student textbook which primarily provides an introduction to (a particular kind of) categorical type theory, but which should also be useful as a reference to those mathematicians and computer scientists pursuing research in related areas. It is envisaged that it could provide the basis for a course of lectures aimed at advanced undergraduate or beginning graduate students. Given the current content of typical British undergraduate mathematics and computer science courses, it is difficult to describe an exact audience at whom the book is aimed. For example, the material on ordered sets should be readily accessible to first and second year undergraduates and indeed I know of courses which contain elements of such topics. However, the material on category theory, while probably accessible to good third year undergraduate students, does require a certain amount of mathematical maturity. Perhaps it is better suited to graduate students in their early stages. Chapters 3 and 4 are probably of second and third year undergraduate level respectively, assuming that the requisite category theory has been assimilated. The final two chapters are probably better suited to first year graduates. In summary, as well as serving as a textbook for (graduate) students, I hope “Categories for Types” will provide a useful reference for those conducting research into areas involving categorical type theory and program semantics.