Resumen de A new foundation for representation in cognitive and brain science: category theory and the hippocampus
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.
It is unreasonable to think that purely linear mathematics can be the killer tool to model the complex interactions that take place in the brain. We may indeed, need a new mathematical language for describing brain activity.
It 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 the 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. The thesis paves the way for a more synthetic methodology in cognitive science, the scale free dynamics hypothesis that is being studied is visited with a new ''categorical" light.
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 gives rise to the ''colimit" which is a place field.
