There are two books that I would highly recommend to any one (especially a high school student or an undergrad with some mathematical maturity) wanting to learn category theory (CT) without necessarily learning all the "abstract nonsense." That is, it is possible to become thoroughly acquainted with a categorical way of thinking, if you will, without learning all the definitions beforehand. The books are "Conceptual Mathematics: A First Introduction to Categories" by Lawvere and Schanuel, the second being "Sets for Mathematics" by Lawvere and Rosebrugh.
The first book (Conceptual Mathematics) is, I believe, the best introduction to CT via sets and functions. From a pedagogical point of view, it is very well-written with lots of examples that slowly but surely develop the diligent student's category-theoretic intuitions. The notion of a functor is only mentioned in the middle of the book and that too in the context of a monoid (which is a very nice concept to learn) and that the notion of a natural transformation isn't even mentioned in the book. Indeed, universal mapping properties are introduced two-thirds of the way into the book. However, that does not prevent Lawvere (and Schanuel) from talking about a lot of stuff. One is surprised by how much CT one learns by the time one finishes reading (and solving the exercises in) the book.
The second book (Sets for Mathematics) essentially is a superb exposition on the elementary theory of the category of sets, and the book can be read either after finishing the first book (mentioned above) or in conjunction with it after one has gained some proficiency in understanding and writing (simple) proofs in CT.
Anyway, if your friend really wants to learn CT without getting "bogged down" by all the definitions, then Conceptual Mathematics is the book to read and absorb. The book looks deceptively easy and devoid of a lot of the standard category theoretic content, but nothing could be further from the truth!
Hope this helps.
Best Answer
Paolo Aluffi's Algebra Chapter 0 develops abstract algebra using Category theory from the very beginning. The exposition is very clear and teaches upto and including the derived functor approach to cohomology. The category theory developed here should be more than enough to study sheaves and schemes eventually.
In an answer to your earlier question, Julien Puydt points to (and I second his suggestion) the excellent text by Ravi Vakil. The category theory developed in this text is really all you need; in fact, there is no more than what is needed for purposes of getting started with AG.