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When I wanted to learn set theory in high school, I found Halmos Naive Set Theory book very readable and understandable. But now, at university, I have been searching for a similar book in category theory, but I haven't found any book like that until now.

What is your suggestion?
Thanks in advance.

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    $\begingroup$ What sorts of features are you looking for? There is a nice MO thread here. $\endgroup$
    – Hoot
    Jul 4, 2016 at 22:54
  • $\begingroup$ @Hoot thanks for the link. I had read that before I asked this question, but I can't read all of them! It's difficult to me to explain explicitly that what features I'm looking for, but every body who read Haloms's book probably knows that what features I'm looking for! $\endgroup$
    – A_Sh
    Jul 4, 2016 at 23:08
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    $\begingroup$ maths.ed.ac.uk/~aar/papers/maclanecat.pdf $\endgroup$
    – Will Jagy
    Jul 4, 2016 at 23:31
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    $\begingroup$ math.mit.edu/~dspivak/teaching/sp13/CT4S.pdf $\endgroup$
    – Will Jagy
    Jul 4, 2016 at 23:35
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    $\begingroup$ @WillJagy I'm very grateful to you for the links, but why you didn't put these comments as an answer? $\endgroup$
    – A_Sh
    Jul 4, 2016 at 23:40

3 Answers 3

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Right; at college level, before, especially, algebraic topology, you are probably best off with something like SPIVAK. Also available as a pdf is Mac Lane, written by one of those who invented category theory, as something of an outgrowth of homological algebra. The latter is probably intended for graduate students. Meanwhile, it would not be surprising if there were still other books, at various levels. Category theory has become indispensable for, say, algebraic geometry.

Some nice reviews for an introductory book: CONCEPTUAL then, with common author Lawvere SETS

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  • $\begingroup$ @Ab_Sh found two more. Since you are reading on your own, start with the lightest reading, probably Spivak. $\endgroup$
    – Will Jagy
    Jul 5, 2016 at 1:29
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    $\begingroup$ At the first glance Shcanuel's book seems very interesting to me, but I found Mac Lan's book in the spirit of Halmos's book! $\endgroup$
    – A_Sh
    Jul 5, 2016 at 1:50
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Doing a Google search for "naive category theory", here the first hit:

Fibered Categories and the Foundations of Naive Category Theory

www.jstor.org/stable/2273784 JSTOR by J Bénabou - ‎1985 - ‎Cited by 191 OF NAIVE CATEGORY THEORY. JEAN BENABOU.

Introduction. Any attempt to give "foundations", for category theory or any domain in mathematics, could ...

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  • $\begingroup$ Here is the pdf file. $\endgroup$
    – A_Sh
    Jul 5, 2016 at 1:53
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    $\begingroup$ This is not going to be readable for a beginner, $\endgroup$ Jul 5, 2016 at 4:35
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Leinster recently came out with a fantastic book

Basic Category Theory, Tom Leinster, 2014

It is shallow in terms of proofs but it is deep with examples. This really will help you understand category theory from whichever mathematics you may already know best.

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