  This paper discusses a simple and explicit toy-model example of the
categorical Hopfield equations introduced in previous work of Manin and the
author. These describe dynamical assignments of resources to networks, where
resources are objects in unital symmetric monoidal categories and assignments
are realized by summing functors. The special case discussed here is based on
computational resources (computational models of neurons) as objects in a
category of DNNs, with a simple choice of the endofunctors defining the
Hopfield equations that reproduce the usual updating of the weights in DNNs by
gradient descent.
