It is often the case that one Ramsey problem is solved by encoding a problem in one already solved and transferring the solution back. In that vein, one can consider the latter Ramsey theorem to be stronger that the former. In recent years, there have been attempts to find general notions for such a procedure. One of them, a semi-retraction, was introduced by Lynn Scow, whose primary motivation was a study of generalized indiscernible. Together with Scow, we found the most general conditions on countable structures under which a semi-retraction transfers the Ramsey property, and more generally Ramsey degrees, from one structure to another. We will compare this notion to the category theoretic notion of pre-adjunction studied by Dragan Ma?ulovi?.