I'd add to this list Algebra, Chapter 0 by Aluffi. It's very clearly-written, even for a total beginner like me, but not dumbed down at all, and has a boatload of exercises which IMO is very helpful for learning the material. While its focus is on algebra and not specifically a textbook on category theory, it introduces categories very early on and, to me anyway, explains them as well as or better than any other treatment I've read.
This text presents an introduction to algebra suitable for upper-level undergraduate or beginning graduate courses.
In this text, categories are introduced around p. 20, after a scant reminder of the basic language of naive set theory, for the main purpose of providing a context
for universal properties. These are in turn evoked constantly as basic definitions are introduced. The word ‘universal’ appears at least 100 times in the first three
chapters.
In my experience if you have or are willing to invest on the side to gain the necessary abstract algebra background then MacLane's Categories for the Working Mathematician is the go to source.
It is certainly "for the Working Mathematician", so don't make bones about that, but to not include it in a reading list is criminal. If nothing else, buy it and keep rereading it from the beginning as a barometer for how much you're learning. As you penetrate it more and more you can judge that as meteoric increase in understanding.
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[ 25.0 ms ] story [ 1035 ms ] threadThis text presents an introduction to algebra suitable for upper-level undergraduate or beginning graduate courses.
In this text, categories are introduced around p. 20, after a scant reminder of the basic language of naive set theory, for the main purpose of providing a context for universal properties. These are in turn evoked constantly as basic definitions are introduced. The word ‘universal’ appears at least 100 times in the first three chapters.
That means Pinter's book is more elementary.
It is certainly "for the Working Mathematician", so don't make bones about that, but to not include it in a reading list is criminal. If nothing else, buy it and keep rereading it from the beginning as a barometer for how much you're learning. As you penetrate it more and more you can judge that as meteoric increase in understanding.
http://mitpress.mit.edu/books/basic-category-theory-computer...