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Algebra Hardcover – January 1, 1970
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Now there's a little oddity about what is really meant by "category theory". Someone informed me a couple of months ago that I had made a grave error in my own definition of ring epimorphisms. Apparently the really modern definition of an epimorphism in category theory requires the right cancellative property. (And monomorphisms require the left cancellative property. See wikipedia for details.) But this book by MacLane and Birkhoff (page 38) uses the old-fashioned definition, which only requires surjectivity. In the case of the ring category, it makes a big difference. (The old-fashioned epimorphism definition is also given by Seth Warner "Modern algebra", page 82; Lang "Algebra", page 120; Grove "Algebra", pages 8, 49, 127; Ash "Basic abstract algebra", pages 19, 37, 89.) So if you want to use MacLane and Birkhoff for category theory, beware of this difference.
It seems to me as a non-algebraist that category theory was introduced as a kind of "grand unified theory" to implement bulk handling of algebraic categories. But in my opinion, it is the differences between the categories which make them interesting, and when category theory is applied to locally Cartesian spaces, C^k differentiable manifolds and fiber bundles, for example, the effort required to fit the categories into the general framework of morphisms and functors is alien to the nature of the objects under study.
In conclusion, if you don't have this book, you're not an algebraist. And if you're some other kind of mathematician, it is the best all-round reference for all of the basic categories of modern abstract algebra. This book has pretty much everything a non-algebraist would want to know about the broad sweep of algebra. It even has chapters on multilinear and exterior algebra and affine spaces. It's a tidy, carefully-written reader-friendly book which tries to help the reader, not show off the superior genius of the authors as some frustrating books do.
By the way, as I understand it, MacLane only introduced the space between Mac and Lane because his wife couldn't type a capital letter in the middle of a word. I think that's a silly reason to change the spelling of one's name. So I spell it in the traditional way as "MacLane". Honi soit qui mal y pense!
I haven't read all the way through, it gets to some advanced (graduate-level) material.