[kian]

Does step help when thinking of the objects as individual data elements, the arrows as cons-links, map being a functor that respects cons-links [i.e. does not change the structure of the list]? The problem here is that implying process, ordering, or anything else is too narrow of a definition for what an arrow/morphism can be used to represent. That's why arrow (a thing that points to another thing), or morphism (a thing that helps define the shape) are actually better terms. Because Category Theory isn't about the things, it's about the relationships between the things, how these can be composed, and how higher-order operators that respect these relationships [and the new ones they represent for even higher-order operators] can form new relationships which can also be composed.