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I am interested in elementary algebra texts and/or notes that place early and continuous emphasis on universal constructions, functors and other aspects of category theory. One text that takes this approach is Aluffi's Algebra: Chapter 0.

Another text that emphasizes universal constructions early-on is Hu's Elements of Modern Algebra

Are there other elementary algebra texts and/or notes that integrate universal constructions and principles of category theory into the development of the subject?

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3 Answers 3

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The two examples that come to my mind are:

Saunders Mac Lane, Garret Birkhoff: Algebra

Peter Hilton, Yel-Chiang Wu: A course in modern algebra

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I think Anderson and Fuller's Rings and Categories of Modules does a bit of that, but only for rings and modules (and not groups or anything else algebraic.)

Grillet's Abstract algebra has universal constructions scattered throughout, but I don't know if it reached your threshold for having enough category theory.

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+1 for my current favorite graduate level general algebra text. Grillet to me is what Lang should be: totally modern, crystal clear,comprehensive and yet of managable size for a 2 semester algebra sequence for first year graduate students. –  Mathemagician1234 Jun 11 '12 at 7:24
Well, I've spent some time looking at Grillet's text and, though it is nice, saves up most of the category theory until the last chapter of the text rather than weaving it through the fabric of the text itself. It does, however, emphasize universal constructions which is at least part of what I'm looking for. –  ItsNotObvious Jun 11 '12 at 20:39

You may be interested in reading Hungerford, but there are better books treating homological algebra at a more advanced level, so it depends on your personal interest. Also picking up a random book in the library and read it is not so bad as it may sound. For general reference you may use Dummit&Foote, which should be standard.

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