I would like a book or PDF file that teaches the basics of category theory using basic abstract algebra (groups, rings and modules) as an example.

For me, the ideal book is "Algebra: Chapter 0", written by Paolo Aluffi. I'd like something as similar as possible to this book. I don't use this book because unfortunately I don't have money at the moment to buy it. I also don't want to download an illegal copy of that book because it is piracy.

Could somebody please indicate me some free (or at least cheap) material similar to that book?

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    $\begingroup$ Have you considered a university library? $\endgroup$ – David C. Ullrich Jun 22 '19 at 20:20
  • $\begingroup$ Yes, but unfortunately no library in my city has that book (yes, I've checked the websites of all the libraries I know). $\endgroup$ – rfloc Jun 22 '19 at 20:23
  • $\begingroup$ @DavidC.Ullrich I even asked AMS Bookstore for a discount coupon for that book, but unfortunately they didn't give it to me. $\endgroup$ – rfloc Jun 22 '19 at 20:28
  • $\begingroup$ @rfloc Did you ask if they could do an interlibrary loan? $\endgroup$ – Derek Elkins left SE Jun 22 '19 at 21:11
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    $\begingroup$ This page gives a list of books and lecture notes available online on category theory. Maybe something there could help you... $\endgroup$ – Arnaud D. Jun 23 '19 at 20:51

A great and accessible book which introduces the basic ideas is Basic Category Theory by Tom Leinster, which is made freely available in PDF format on ArXiV.

He uses algebraic structures such as groups and modules, as well as topological spaces in most examples.

  • $\begingroup$ I had already seen this PDF and I consider it good. But I'm hoping to find something more similar, and free, to that book I mentioned. $\endgroup$ – rfloc Jun 22 '19 at 20:19
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    $\begingroup$ There is also this, which is a pdf of this. If you want a "free" pdf book, you'll probably best looking for course notes on professors' websites, such as the one I've attached in this comment. $\endgroup$ – Luke Collins Jun 22 '19 at 20:21
  • $\begingroup$ I didn't know this one. I'll see if it' s good! $\endgroup$ – rfloc Jun 22 '19 at 20:25

I have never really looked into it myself, but I once found "Category Theory in Context" by Emily Riehl, which can be downloaded from her university webpage. The title at least suggests that it might be worth a try for you.


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