Talking about catjects, we are looking for morphisms. The question is, what is turning a form into a form. We had objects relying on their own, thanks to creation and nature, to define their form. We had subjects borne by reason, to bring form to about anything. Now it is catjects. Catjects define the way observers are necessary to determine the indeterminate. Catjects are about the relation of a thing to an observer, to become a thing, and to become an observer.
These catjects must be functors, framing relations. Whitehead proposes to look at 'creativity,' 'one,' and 'many' as possible candidates for that kind of functors. They seem to catch the way an entity, looked at by an observer, occasions itself, exhibiting self-identity and self-diversity in order to combine reference with nexus.
The subject is a superject in that whithout its determination of a thing nothing is actual, and nothing actually is. But this superject in turn is nothing without indeterminateness looking at it and challenging it to determinate it. Morphisms would us allow to define the network patterns any one object, and subject, relies upon to be what it is. We touch upon venerable endeavours here, since attempts to define the self-similarities of music, picture, text go back to Aristotle at least. I am not sure whether the wealth of data produced by the use of computers in searching and indexicalizing media of all kinds will help to solve that riddle.