I've been thinking that the point of category theory is to reexpress facts about the internal structure of objects as facts about the external relationships between objects. And to focus on the latter relationships as more relevant.

In other words, an object is a black box. So I'm thinking of what it would mean to rethink the basics of category theory in terms of black boxes.

*In science, computing, and engineering, a black box is a device, system or object which can be viewed in terms of its inputs and outputs (or transfer characteristics), without any knowledge of its internal workings. Its implementation is "opaque" (black). Almost anything might be referred to as a black box: a transistor, an algorithm, or the human brain.* (Wikipedia)

Apparently, there is quite a bit of math in system theory related to black boxes, but the page does not reference category theory.

I think the black box concept is helpful in trying to study equivalences, equalities, identities, etc. It does away with the usual baggage of unspecified collections that I think discredits set theory and category theory. Instead of claiming that there is a set/class/category/collection of "sets" which includes {black cow, brown cow, white cow} and {mama pig, baby pig} and so on, every set would be a black box. If you needed to talk about its elements or subsets or components or features, then those would be black boxes, too.

Then I think it's much easier to focus on all the relevant questions. For example, in what senses are two black boxes equivalent or not?

In other words, an object is a black box. So I'm thinking of what it would mean to rethink the basics of category theory in terms of black boxes.

Apparently, there is quite a bit of math in system theory related to black boxes, but the page does not reference category theory.

I think the black box concept is helpful in trying to study equivalences, equalities, identities, etc. It does away with the usual baggage of unspecified collections that I think discredits set theory and category theory. Instead of claiming that there is a set/class/category/collection of "sets" which includes {black cow, brown cow, white cow} and {mama pig, baby pig} and so on, every set would be a black box. If you needed to talk about its elements or subsets or components or features, then those would be black boxes, too.

Then I think it's much easier to focus on all the relevant questions. For example, in what senses are two black boxes equivalent or not?