In a previous article, we defined the concept of RNmatrices, generalizing that of Nmatrices, and have provided finite semantics, as well as corresponding decision methods, for the hierarchy of paraconsistent logics \(C_{n}\) by da Costa (also called C-systems). Here, we extend this initial study on RNmatrices for \(C_{n}\) , applying to them the methodology of swap-structures and obtaining from this a new class of models capable of characterizing the family of C-systems. We give a brief algebraic and combinatorial (for the finite structures) description of the elements of the RNmatrices of this class of models for \(C_n\) . Finally, we present a notion of category of (arbitrary) RNmatrices. When applied to the specific case of the RNmatrices modeling \(C_{n}\) , we show that this category is in fact isomorphic to the category of non-trivial Boolean algebras. Two other categories of restricted swap structures related to \(C_n\) are also investigated, one of them being equivalent to the category of non-trivial Boolean algebras with homomorphisms of implicative lattices as morphisms.