Representations of algebras in varieties generated by infinite primal algebras

If \({\mathcal{A}}\) is an infinite primal algebra, then we shall represent any algebra in the variety \({V\,(\mathcal{A}}\) ) generated by \({\mathcal{A}}\) as a limit reduced power of \({\mathcal{A}}\) . Furthermore, we show that any homomorphism between algebras in \({V\,(\mathcal{A}}\) ) can be induced by mappings between underlying sets of the limit reduced powers. With this representation of the morphisms between algebras in \({V\,(\mathcal{A}}\) ) at hand, we will construct a category equivalent to the category \({V\,(\mathcal{A}}\) ).