Showing that the Ramsey property holds for a class of finite structur es K can be an extremely challenging task and a slew of sophisticated metho ds have been proposed in literature. These methods are usually constructive : given A, B in K and k>=2 they prove the Ramsey property directly by const ructing a structure C in K with the desired properties. It was Leeb who poi nted out already in early 1970's that the use of category theory can be qui te helpful both in the formulation and in the proofs of results pertaining to structural Ramsey theory. Instead of pursuing the original approach by L eeb (which has very fruitfully been applied to a wide range of Ramsey probl ems) we proposed in the last few years a set of new strategies to show that a class of structures has the Ramsey property.

In this talk we explici tly put the Ramsey property and the dual Ramsey property in the context of categories of finite structures. We use elementary category theory to gener alize some combinatorial results and using the machinery of very basic cate gory theory provide new combinatorial statements (whose formulations do not refer to category-theoretic notions) concerning both the Ramsey property a nd the dual Ramsey property. DTSTAMP:20220808T065746Z DTSTART;TZID=Europe/Budapest:20180509T100000 DTEND;TZID=Europe/Budapest:20180509T120000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR