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This I'm a third year undergraduate student majoring computer science and minoring mathematics. I'm interested in topos theory both from logical and geometrical point of view. I've seen this book being suggested in various places, such as Topos in nLab and this introduction with programmatic reading plan by John Baez. For this purpose I'm currently learning rudiments of category theory from Awodey's Category Theory book and haven't read anything else before. There's also this similar question asking about prerequisites for topos theory, which is more general for me who is aiming to read this specific book.

I wanted to ask for suggestions for programmatic reading plan that covers sufficient (and ideally, necessary) material which ables someone to go through this book without much difficulty.


Edits

As @KevinArlin mentioned, Baez's reading plan is provided for learning general advanced topos theory, which is also the subject of this specific book and therefore it's a suited suggestion. But I was willing to see more/other suggestions here from those who have read this book.

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    $\begingroup$ Did you read Baez's post? Where he says it took him, an excellent mathematician, many years to get to a point of comfort with this book? It's extremely over-ambitious to hope to jump from Awodey to Johnstone. Don't do that, unless you're working individually and intensively with an expert in the field, in which case you shouldn't need our advice. Anyway, to answer your question, Baez has already provided a good reading plan aimed at advanced topos theory. You could potentially skip the first couple of entries. $\endgroup$ Jun 5, 2021 at 17:28
  • $\begingroup$ @KevinArlin Yes I've read that post. Also I agree that I cannot instantly jump to Johnstone. I'm not sure if the reading plan provided by Baez is exclusively specialized for this specific book; it was meant to be aimed at topos theory in general as you said. So I could imagine that for my purpose, there might be a different (and probably shorter) way from the one he provided. But if you don't think so and believe that all readings suggested by Baez are needed, I will be happy if you let me know. $\endgroup$
    – Kooranifar
    Jun 5, 2021 at 18:16
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    $\begingroup$ The specific book is a treatment of topos theory in general, so I don’t understand the distinction. Anyway, yes, you should start somewhere higher up on that list. Few undergrads would succeed with anything more advanced than Mac Lane-Moerdijk without significant guidance, and even that is really a graduate-level text. $\endgroup$ Jun 5, 2021 at 21:01
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    $\begingroup$ Before trying to read Sheaves in geometry and logic, but after reading Awodey, try reading Categories for the working mathematician. It is also a general category theory textbook, but it is more advanced and more mathematical than Awodey's book. If you are at the point where CWM is comfortable reading then perhaps you are ready to learn topos theory, but otherwise keep learning category theory fundamentals. $\endgroup$
    – Zhen Lin
    Jun 5, 2021 at 22:16
  • $\begingroup$ @ZhenLin Can you explain what you mean by "more mathematical"? $\endgroup$ Jun 6, 2021 at 8:04

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I agree with Zhen Lin’s and Baez’s recommendations. You will need more comfort than just the rudiments in general category theory to learn topos theory. After that, start topos theory no further down Baez’s list than Mac Lane-Moerdijk. It is generally a very good idea to try to have somebody you can talk about this material rather than learning from books alone, but there is a lot of categorical conversation online that might help with this process if that’s impossible; you can read old conversations on the nCategory Cafe or perhaps join the category theory Zulip channel (not sure how active it still is, but you can find references to it on Baez’s site.)

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    $\begingroup$ I would like to add that you should not at all feel that not reading the most difficult and advanced books on a subject is some kind of admission of defeat, or that people who suggest otherwise are looking down on you. MacLane and Moerdijk's book is a real mathematics book, with already a lot in it to digest. If you have a good understanding of its contents, you definitely know a thing or two about topos. $\endgroup$ Jun 29, 2021 at 15:18
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    $\begingroup$ @CaptainLama Yes, that's a very valuable point, one I wish I'd learned better myself at a younger age. $\endgroup$ Jun 29, 2021 at 17:14

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