Before revision:  We prove a complete panel of results required for the analysis of discretisation schemes for partial differential equations based on this complex: exactness properties, uniform Poincar\'e inequalities, as well as primal and adjoint consistency.
After revision:  We prove a complete panel of results for the analysis of discretisation schemes for partial differential equations based on this complex: exactness properties, uniform Poincar\'e inequalities, as well as primal and adjoint consistency.