A FRT type construction is done in a minimal categorical context: the ambient monoidal category is only assumed to have coequalizers. The early motivation for this construction was G. Militaru's work on the D-equation. We get generalizations of Militaru's constructions and results. The D-equation is also studied using the classical FRT construction: this leads to a notion of D-bialgebra. New solutions of the D-equation are constructed.