I'm trying to understand the Homotopy Type Theory book. I find myself completely lost in Chapter 2, especially when it starts using higher groupoids.

What is the recommended background for this book? I once studied abstract algebra (and even remember a bit) same with topology, but not category theory. I skimmed a topology book recently to refresh my memory, but I'm realizing that the topology in the HoTT book is algebraic topology and I haven't studied that before.

My general question how can I fill the gaps in my background knowledge so that I can make sense of this book?

More specifically for Chapter 2, what is a good introduction to higher groupoids? Should I expect to learn about those by studying algebraic topology or category theory?

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    $\begingroup$ Join the club! The HoTT book "was written as a massively collaborative effort by a large number of people", and does read as if it was written for the in-crowd. It is surely tougher going than the authors collectively intended as they try to spread the word, in part because you are left running here and there to try to catch up on what they are taking for granted. $\endgroup$ Oct 11, 2013 at 6:59
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    $\begingroup$ You will not learn about higher groupoids by studying algebraic topology or category theory, at least not at the introductory level. Rather, I advise you to just ignore the phrase entirely and replace it with ‘space’ – that, after all, is the content of the homotopy hypothesis. $\endgroup$
    – Zhen Lin
    Oct 11, 2013 at 7:10

1 Answer 1


Your question was asked in October, so maybe you no longer need help... but for anyone who does, I highly recommend Bob Harper's video lectures on HoTT. (Which are from a graduate research seminar he taught at Carnegie Mellon. Lecture notes and hw problems are also available. The course was offered in the Computer Science department and there aren't really any pre-requistes aside from basic mathematical maturity. No need to study algebraic topology or category theory beforehand.) http://www.cs.cmu.edu/~rwh/courses/hott/

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    $\begingroup$ Yes, that course is helping me. Bob also uses a lot of CT terminology. For that you can find Awodey's lectures: youtube.com/watch?v=ZKmodCApZwk $\endgroup$ Jan 8, 2014 at 21:59

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