Rat between two walls viewed as a product in a category
According to the author, in this maze-category the objects are memories (or mental objects). 

The author references to chapter 3, when discussing the maze-category. Chapter 3 of the book, gives an application to Memory Evolutive Neuronal Systems (MENS). There, a morphism represents a way of relating mental objects. This is a general description. 

The author gives as examples for the maze-category:


travel time 
number of steps needed to go from one mental object to another.


The product $P$ of two memories is two memories at once. The concept of a middle point requires that the agent has the memories of both memories. One wall only requires one memory.

$X$ can potentially represent any of the points between the two walls.