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[QUOTE="mathwonk, post: 5547685, member: 13785"] i would suggest that you mainly want to know what a functor is, and a natural transformation, a representable functor, and then Yoneda's lemma. That's about it, as far as I am concerned. Oh and I guess you want to know the categorical definitions of isomorphisms, products and sums (coproducts), as well as inverse and direct limits. edit: My viewpoint is that of an algebraic geometer who is not a category theorist. So to me most of the stuff in the free book you linked is totally unnecessary verbiage. As a youngster I recall thinking category theory was a lot of fun, but as a practicing mathematician, it seemed like (to quote one somewhat cranky and opinionated algebraic geometer, Miles Reid, p.116, Undergraduate Algebraic Geometry) "surely one of the most sterile of all intellectual pursuits". This in the vein of the earlier question of what are your goals. I.e. if your goal is to be a mathematician in a field other than category theory, you will not need all this technical terminology. But if you enjoy this pursuit, then wonderful. Go for it. I would actually recommend reading the original paper that started the theory, at least the introduction: [URL]http://www.ams.org/journals/tran/1945-058-00/S0002-9947-1945-0013131-6/S0002-9947-1945-0013131-6.pdf[/URL] [/QUOTE]
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