I strongly disagree. From experience teaching category theory to undergraduates, it is totally obtuse before that have a large pool of examples on which to draw

I strongly disagree. From experience teaching category theory to undergraduates, it is totally obtuse before that have a large pool of examples on which to draw. In a very first course, students are still struggling to learn concepts from linear algebra, which will be the bread and butter of the rest of their mathematics. In a second course, they are struggling to learn why the definition of "linear map" is different from the definition of "matrix" they learned in their first course. You could say the same thing about metric spaces or topology. Perhaps the third course is a nice place to start introducing some category theory, since they will now have actual examples on which to draw, and learn about the unifying concepts of "morphism", "categorical product", and so on. They might even be ready for some interesting functors, such as the fundamental group of a topological space. If you were to teach category theory as a very first course, what would you teach? What examples of categories do you have? What examples of functors?