  Now let us provide a notation, inspired by Ajdukiewicz, for the category of a functor such as ‘\(F\)’. If the category of ‘\(a_1\)’ is \(\alpha_1\), the category of ‘\(a_n\)’ is \(\alpha_n\), and the category of the whole expression ‘\(F(a_1 \ldots a_n)\)’ is \(\beta\), then the category of the functor expression ‘\(F\)’ we write as