Yes. But my more important point is that you can tach about these mappings in isolation, in the context of functional programming. No Category Theory needed.

You can teach about "different sorts of mappings" in just about any setting. In fact, that's kind of the whole reason Category Theory exists. So why teach the general result when all you care about is its application to functional programming?

The importance of structure preserving mappings shows up in many other places besides functional programming. I do believe context is important, but having multiple contexts is even better.

> but having multiple contexts is even better.

Given the investment necessary to make this jump, I believe that the benefit outweighs the cost for most.

You don't need to teach category theory proper to get the idea. So I think we are in agreement :)