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I have a background in theoretical computer science (in type theory) but not pure mathematics and I just finished reading Steve Awodey's Category Theory. I am hoping to explore higher category theory but I don't have a background in topology. What books/pre-requisites about algebraic topology/higher category theory might be helpful for me? Many Thanks.

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    $\begingroup$ Just out of curiosity, why are you interested in learning about higher category theory? $\endgroup$
    – Frederik
    Commented Jun 24, 2021 at 23:47

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The step from category theory to higher category theory is quite large, and i think higher category theory is a very difficult subject to approach. It is a very deep and complicated theory. The most normal way to learn it would be through quasicategories which employs the theory of simplicial sets. Rather than reading "Higher Topos Theory" by Lurie i would properly start reading "Introduction to Infinity Categories" by Markus Land.

I do not think this strictly requires algebraic topology, but i do not really see why one would be interested without knowing a least some basic homotopy theory at this time. The definitions will also look very strange when one does not know the notion of a homotopy. I would probably recommend to at least know a bit about the higher homotopy groups. I think reading the first 10 chapters of Peter May's book "A Concise Course in Algebraic Topology" should be the most direct way. I also think it would be beneficial to read some of the first chapter of "Simplicial Homotopy Theory" by Georss-Jardine, to get an introduction to simplicial sets before diving in. Both of these books are freely available on the internet.

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    $\begingroup$ Presumably the OP is interested because of homotopy type theory. $\endgroup$ Commented Jun 24, 2021 at 23:50
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If you're interesting in homotopy type theory, you should try to read the HoTT book and then learn a proof assistant. To read books on algebraic topology and higher categories written for mathematicians would probably feel a lot like trying to learn ancient Greek. Possible, but a definite multi-year effort.

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