We present work whose ultimate goal is the creation af o wide-coverage abstract categorical grammar (ACG) that could be used to automatically build discourse-level representations. In our work, we advance towards that goal by laying down the foundations necessary for building wide-coverage ACGs. We first examine existing language resources, in particular the Frigram interaction grammar and its lexicon Frilex, and assess their utility to building a wide-coverage. ACG. We then present our implementation of the ACG machinery wich allows us to experiment with grammars lexicalized by Frilex. Finally, we consider the challenge of integrating the treatment of disparate linguistic constraints in a single ACG and porpose a generalization of the formalism : graphical abstract categorical grammars. The report concludes with an exploration of some of the formal properties of graphical ACGs.