Showing that the Ramsey property holds for a class of finite structures can be an extremely challenging task and a slew of sophisticated methods have been proposed in literature.In this paper we propose a new strategy to show that a class of structures has the Ramsey property. The strategy is based on a relatively simple result in category theory and consists of establishing a pre-adjunction between the category of structures which is known to have the Ramsey property, and the category of structures we are interested in.We demonstrate the applicability of this strategy by providing short proofs of three important well known results: we show the Ramsey property for the category of all finite linearly ordered posets with embeddings, for the category of finite convexly ordered ultrametric spaces with embeddings, and for the category of all finite linearly ordered metric spaces (rational metric spaces) with embeddings.

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A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Nešetřil introduced a relaxed version of homogeneity: we say that a structure is homomorphism-homogeneous if every homomorphism between finite substructures of the structure extends to an endomorphism of the structure. In this paper we characterize homomorphism-homogeneous partially ordered sets (where a homomorphism between partially ordered sets A and B is a mappingf (y)). We show that there are five types of homomorphism-homogeneous partially ordered sets: partially ordered sets whose connected components are chains; trees; dual trees; partially ordered sets which split into a tree and a dual tree; and X 5 -dense locally bounded partially ordered sets.

In 2012 M. Sokić proved that the class of all finite permutations has the Ramsey property. Using different strategies the same result was then reproved in 2013 by J. Böttcher and J. Foniok, in 2014 by M. Bodirsky and in 2015 yet another proof was provided by M. Sokić.Using the categorical reinterpretation of the Ramsey property in this paper we prove that the class of all finite permutations has the dual Ramsey property as well. It was Leeb who pointed out in 1970 that the use of category theory can be quite helpful both in the formulation and in the proofs of results pertaining to structural Ramsey theory. In this paper we argue that this is even more the case when dealing with the dual Ramsey property.

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