The dualities between and , where X and W are two sets and (i.e., the mappings satisfying for all and all index sets ), can be ‘represented’ with the aid of functions . Here the paper shows that they can be also represented with the aid of functions , where . As an application, it shows that every duality is completely determined by a suitable duality between and (i.e., a mapping satisfying for all and all index sets ), applied to the epigraphs of the functions.