Finite Ramsey theory through category theory

Abstract

We present a new, category-theoretic point of view on finite Ramsey theory. Our aims are as follows:

• to define the category-theoretic notions needed for the development of finite Ramsey
• to state, in terms of these notions, the general fundamental Ramsey results (of which various concrete Ramsey results are special cases); and
• to give self-contained proofs within the category-theoretic framework of these general results.

We also provide some concrete illustrations of the general method.