A preliminary version of these notes formed the basis of four lectures given at the Summer School on Generic Programming, Oxford, UK, which took place during August 2002. The aims of the notes are to provide an introduction to very elementary category theory, and to show how such category theory can be used to provide both abstract and concrete mathematical models of syntax. Much of the material is now standard, but some of the ideas which are used in the modeling of syntax involving variable binding are quite new. It is assumed that readers are familiar with elementary set theory and discrete mathematics, and have met formal accounts of the kinds of syntax as may be defined using the (recursive) datatype declarations that are common in modern functional programming languages. In particular, we assume readers know the basics of λ-calculus. A pedagogical feature of these notes is that we only introduce the category theory required to present models of syntax, which are illustrated by example rather than through a general theory of syntax.
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