I can recommend several much better sources that will ease your transition into both abstract algebra and category theory, Silva.

Lang is far too difficult for a first brush with abstract algebra, and MacLane is even MORE difficult for a neophyte in algebra. Category theory has VERY far-reaching conceptual implications for most of modern mathematics, not just algebra. So no, in principle, you don't have to learn abstract algebra to learn it, but that's where most mathematicians have infused it. This is because it's natural to organize types of structures into categories and that's really what algebra is all about: types of structures, i.e. sets with binary relations on them.

There are a legion of great abstract algebra texts, but my favorite is E. B. Vinberg's A COURSE IN ALGEBRA, available through the AMS. It takes a very concrete, geometric approach and builds an extraordinary amount of algebra from first principles all the way up to the elements of commutative algebra, Lie algebras and groups and multilinear algebra. It will help you learn a great deal of algebra very quickly and without the confusion of learning category theory simultaneously. Another geometrically flavored-but a bit more challenging-book is the classic ALGEBRA by Micheal Artin. Indeed, I think the 2 books compliment each other very nicely. Mastering both books will give you a very good working knowledge of algebra and you'll be more than ready to tackle Lang's book after that.

As for category theory, the best introductory text I know is CATEGORY THEORY by Steven Awodey. Gentle, rigorous and masterly, it's the best book for undergraduates and the only one I'd use for a beginning course in category theory for students that don't have strong backgrounds in algebra. It's pricey, but totally worth it. One other very good-and short-book you should look for and I heartily recommend is T. S. Blyth's CATEGORIES—a terrific short introduction for any student with good mathematics background that wants just the basics in category theory. It's REALLY hard to find now, but if you can get a copy, by all means do so.

That should help you out. Good luck!

theorybefore you learn undergraduate algebra is about as far-fetched as any study plan I have ever heard of. $\endgroup$5more comments