Cooperation between firms can never improve the technical efficiency of any coalition of firms. This standard result of the productivity measurement literature is based on the directional distance function computed on firm groups. Directional distance functions are usually defined on the standard sum of input/output vectors. In this paper, the aggregation of input/output vectors is generalized thanks to an isomorphism in order to capture three results: the cooperation improves technical efficiency ; the cooperation reduces technical efficiency ; and finally the cooperation between firms yields no variation of technical efficiency, i.e. , the distance function is quasi linear. The improvement of technical efficiency is shown to be compatible with semilattice technologies. In this case, the firms merge according to their inputs only because constraints are imposed on outputs, and conversely, they may merge according to the outputs they can produce because some limitations are imposed on the use of inputs.