[NOTE: For reasons that I hope the question below will make clear, I am interested only in answers from those who have read Mac Lane's Categories for the working mathematician [CWM], or at least have a solid grasp of the minimal mathematical background that a prospective reader would have to have in order to profit from its exposition.]
I would like to read Mac Lane's CWM but I'm stymied by the fact that a great many (if not most) of Mac Lane's examples come from areas of mathematics I know little or nothing about. (I can't make any sense of category-theory writing without the aid of copious examples, so skipping Mac Lane's would be pointless for me.)
For example, algebraic topology and homological algebra seem to be greatly favored by Mac Lane as sources for illustrative examples. I could adopt the strategy of simply reading standard, full-length textbooks on these subjects (of which there's certainly no shortage to choose from), but this would take me many months, which is more than I want to devote to such preparatory reading, plus I suspect it may be overkill anyway.
(I should clarify that, when it comes to mathematical subjects that I'm completely unfamiliar with, I just have to read books from the beginning. IOW, I can't simply take the tack of consulting one of such books (or Wikipedia, etc.) as a reference whenever I ran into some unfamiliar example in CWM, and selectively looking up whatever I did not understand. At best, such a narrowly targeted excursion would fill me in some definitions, but it would almost certainly fail to make the example any more useful as an illustration of an abstract concept than it was before. I find examples useful only when I have some familiarity with the example's "case study".)
My only remaining hope is to find introductions to these subjects that are not only brief, but also (and this is crucial) that focus on those areas of their subjects from which Mac Lane draws his examples. (The reason the last requirement is my having found that the little algebraic topology that I know, which I learned several years ago from an introductory treatment by Henle, is of little help to me when I confront Mac Lane's algebraic-topology-based examples in CWM, which suggests to me that the focus of Henle's intro is not particularly well aligned with Mac Lane's point of view.)
EDIT: I'm comfortable with the basics of set theory, general group theory (shakier grasp of rings, monoids, abelian groups), general/point-set topology (first 2/3 of Munkres' book), real analysis (shakier with complex analysis and measure theory), linear algebra and linear/vector spaces, posets.
Thanks!
Best Answer
All condescension aside, my first thought was that, in fact, category theory is an incredibly useful tool and language. As such, many of us want to read CWM so that we can understand various constructions in other fields (for instance the connection between monadicity and descent, or the phrasing of various homotopy theory ideas as coends, not to mention just basic pullbacks, pushforwards, colimits, and so on). So it is in fact relevant WHY you want to read it.
As an undergraduate, I started reading CWM, with minimal success. The idea being primarily that, as you say, I had very few examples. I thought the notion of a group as a category with one element was rather neat, but I couldn't really understand adjunctions, over(under)-categories, colimits or some of the other real meat of category theory in any deep, meaningful fashion until I began to have some examples to apply.
In my opinion, it is not fruitful to read CWM straight up. It's like drinking straight liquor. You might get really plastered (or in this analogy, excited about all the esoteric looking notation and words like monad, dinatural transformation, 2-category) but the next day you'll realize you didn't really accomplish anything.
What is the rush? Don't read CWM. Read Hatcher's Algebraic Topology, read Dummit and Foote, read whatever the standard texts are in differential geometry, or lie groups, or something like that. Then, you will see that category theory is a lovely generalization of all the nice examples you've come to know and love, and you can build on that.