Here goes a summary of his work in the words of the author himself: The thesis establishes correspondences between mathematical structures and brain structures. The virtue of such a correspondence is that it makes available the powerful tools of the latter for the deduction of hypotheses for structure and function in neuropsychology. Such an approach is relatively free from the vagaries of purely verbal reasoning and can offer novel insights into the intrinsic nature of cognitive phenomena. The thesis sets the agenda of category theory as the appropriate methodology that provides the necessary theoretical framework in order to understand the structure of complex systems, like the brain, in mathematical terms. Although category theory at first sight may seem too pure and universal, in contrast with the spurious biological realm, where the particular prevails over the universal; it may lead to a new and deeper insight into the structure and the representational power of the brain. In addition, it provides a theory of hippocampus structure and function based on category theory. In particular, it demonstrates that the co-operation of the grid fields may give rise to a ``colimit" which is a place field.