In their highly influential work ``Fra\"iss\'e Limits, Ramsey Theory, and Topological Dynamics of Automorphism Groups'', Kechris, Pestov, and Todorcevic characterized fixed point properties of non-archimedean Polish groups using structural Ramsey Theory. Category theoretic methods have demonstrated to be quite effective at both proving Ramsey theoretic results, and generalizing Fra\"iss\'e Theory as witnessed by works of Mašulović and Kubiś respectively. In fact, the Fra\"iss\'e sequence approach of Kubiś has been fruitful in producing a variety of generic structures. Our goal for this talk is to manufacture a correspondence in the vein of Kechris, Pestov, and Todorcevic in the categorical setting with weaker combinatorial hypotheses, but the same dynamical strength. Time permitted, we will also look at some examples. This is a joint work with Adam Bartoš, Tristan Bice, Wiesław Kubiś.