Figure 1: Het d: X→ A-Brain Functors: A mathematical model of intentional perception and action

<p>In the body of this paper, I will try to keep the mathematics at a minimal conceptual level&ndash; which the mathematical formulations restricted to the Appendix. Category theory lends itself to visualization in diagrams so that non-mathematical style of presentation is emphasized by an abundant use of diagrams. A category is intuitively a set of objects of the same type. Morphisms between objects should be thought of as a type of determining relation or cause-effect relation between the objects. When a morphism is between objects of the same category, it is called a homomorphism or hom, and when between objects of different categories it is a heteromorphism or het.4 One of the problems in the conventional treatment of category theory5 is that it tries to ignore heteromorphisms even though hets are a natural part of working mathematics. This leads to certain definitions being rather contrived (to avoid mentioning hets), the usual treatment of the universal mapping properties in adjunctions being the case in point. Adjunctions will be introduced informally and in the natural manner using hets. The general setting is how the objects in one category (e.g., the &quot;environment&quot; in a life sciences context), the &quot;sending&quot; category, will &quot;affect&quot; or &quot;determine&quot; objects in another category (e.g., &quot;organisms&quot;), the &quot;receiving&quot; category. We start with an object X in the sending category, an object A in the receiving category, and a specific het determination d : X &rarr; A from X to A.6</p>