It is important to note that the Categorial framework makes no commitment to how the multi-linear algebraic objects are realized, only a commitment to their shape and how they are combined.
the vector spaces corresponding to atomic categories, such as noun and sentence, do not have to be distributional in the classical sense; they could be distributed in the connectionist sense (Smolensky 1990), where the basis vectors themselves are not readily interpretable (the neural embeddings that we use in this article fall into this category).