  Despite ample evidence that our concepts, our cognitive architecture, and
mathematics itself are all deeply compositional, few models take advantage of
this structure. We therefore propose a radically compositional approach to
computational neuroscience, drawing on the methods of applied category theory.
We describe how these tools grant us a means to overcome complexity and improve
interpretability, and supply a rigorous common language for scientific
modelling, analogous to the type theories of computer science. As a case study,
we sketch how to translate from compositional narrative concepts to neural
circuits and back again.
