0
$\begingroup$

Title is pretty self explanatory. All recommendations welcome. Comments and answers which reject the premise of the question will be met with eye rolling.

If I don't see a good enough answer I'll have to write my own book and I'd love not to do this.

Edit: I'm interested in a category theory books which mostly focus on categories and functors which come from undergrad courses (sets, groups, graphs, vector spaces, R-modules, topological spaces, cartesian spaces, the matrix cat) and those which don't really require any serious heavy lifting to consider (posets, the simplex cat, etc). The ultimate book for me would tie lots of ideas together from various courses for the student.

Improve this question
$\endgroup$
5
  • 3
    $\begingroup$ Let me earn some eye rolling. In my opinion, the best option is something like P. Aluffi's Algebra Chapter 0, which is not a category theory textbook but an algebra textbook heavily using cathegory theory (you might want to add in your question whether you're interested in purely cathegory theory textbooks or also things like this). $\endgroup$
    – Michał Miśkiewicz
    Mar 31 at 19:20
  • 3
    $\begingroup$ I recommend Emily Riehl's Category Theory in Context. She says in the introduction that it grew out of undergraduate courses. It is heavy on examples, but one can skip certain examples that undergraduate students may not be familiar with. It is published by Dover and a free PDF copy is available on the author's website. $\endgroup$
    – Mahdi Majidi-Zolbanin
    Mar 31 at 19:29
  • $\begingroup$ @MichałMiśkiewicz thank you for encouraging me to edit/clarify! $\endgroup$
    – cheyne
    Mar 31 at 22:14
  • 1
    $\begingroup$ @MahdiMajidi-Zolbanin This is currently my go-to text but I think to me it feels empathetic to undergrads but not for undergrads? I dunno. That's definitely my only option right now. $\endgroup$
    – cheyne
    Mar 31 at 22:15
  • $\begingroup$ The best category theory book for an undergraduate student is the book they decide to read on their own. Such students exist and they can't be stopped. Try to talk to them about any other kind of math, they will bring it back to category theory within 10 minutes. I think he read Awoodey if I recall correctly, and there was a series of category theory videos on You Tube which were very influential to his thinking. All of this said, such students are exceedingly rare and precious. $\endgroup$
    – James S. Cook
    Apr 1 at 2:20

4 Answers 4

Reset to default
5
$\begingroup$

This really depends on the group of students you are working with, including their mathematical maturity level and what their interests are.

I think "Sets for Mathematics", by Lawvere, is probably the gentlest introduction.

"Category Theory in Context" is thorough and doesn't assume as much background knowledge as "Categories for the Working Mathematician" by Mac Lane, although I learned from that book as an undergrad myself.

In another direction you could try "Seven Sketches in Compositionality: An Invitation to Applied Category Theory" by Brendan Fong and David Spivak. Not at all systematic, but seems like it would be a really fun romp.

Another completely different direction would be "Category Theory for Programmers" by Bartosz Milewski.

Improve this answer
$\endgroup$
2
  • 1
    $\begingroup$ I love this answer and am familiar with some of these but not others. Let me see what else is suggested for a bit :) $\endgroup$
    – cheyne
    Mar 31 at 22:16
  • $\begingroup$ Just an update: I've now reviewed lots of the books mentioned and I don't think any of them are specifically designed for the "typical" undergraduate student who is interested in mathematics. $\endgroup$
    – cheyne
    Jun 29 at 18:33
3
$\begingroup$

Leinster's Basic Category Theory is quite appropros. It is slightly shorter and slightly easier than Riehls' CTIC and draws examples primarily from a first course in topology, algebra, and order theory.

Awodey has a category theory textbook, extremely accessible with very little background, maybe inteded for first or second year. This is, I believe, still more apropros than Milewski's, which, while interesting, is more from programmers than mathematicians.

Improve this answer
$\endgroup$
3
$\begingroup$

Eugenia Cheng's new book The Joy of Abstraction came out not too long ago. It is an introduction to category theory, intended to bridge the gap between little-to-no undergraduate mathematics and the standard undergraduate category theory texts by Lawvere and Schanuel, Riehl, Leinster, etc.

At this moment a PDF of the prologue for Cheng's book is available for free on the publisher's website, and might help you decide if the goals and intended audience of the book will align with your goals. It could also be that using this book in combination with one of the other standard undergraduate texts (as recommended by others) will meet your needs.

Improve this answer
$\endgroup$
0
$\begingroup$

Don't overlook $n$Lab. It is an excellent open resource for this, and includes a good list of textbooks.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.