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This might be too vague or too broad if we're not careful. Therefore, let's focus on the basics. According to this MSE search, this is new to MSE.

Some Background:

I have read Goldblatt's, "Topoi: A Categorial Analysis of Logic," - although Chapter 14 is where I stopped doing its exercises altogether, which I had been gradually neglecting as I read the text. It covers some ground in its opening chapters.

In this comment on a question of mine, three books on category theory were recommended.

I'm reading Mac Lane and Moerdijk's, "Sheaves in Geometry and Logic: A First Introduction to Topos Theory." Its very first chapter is on categorical prerequisites and I have read it.

Around 2013, I read most (if not all) of Turi's "Category Theory Lecture Notes" from The University of Edinburgh. I've forgotten most of it though.

The Question:

What are the prerequisites for topos theory?

Context:

I am teaching myself topos theory because I find it fascinating and I enjoy the challenge.

I'm not sure where I get this notion from but I'm given to understand that algebraic geometry plays a rôle in topos theory. I did a module on algebraic geometry in the final year of my MMath.

The same goes for topology.

I have included the tag because, as above, some of you might feel it best that I read some other books before continuing with Mac Lane and Moerdijk's.

Please help :)

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    $\begingroup$ I'm not sure if this is a useful comment or not, but I'm currently part way through Lawvere and Schanuel's Conceptual Mathematics, which will introduce me to topos theory by the end, and which starts at almost kindergarten level with absolutely no prerequisites whatsoever. $\endgroup$
    – N. Virgo
    Mar 12 '20 at 15:14
  • $\begingroup$ Related. $\endgroup$
    – Shaun
    Mar 28 '20 at 18:46
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I would follow the advice of the first paragraph of my edition of Mac Lane-Moerdijk, which is to go read sections of Mac Lane's Categories for the Working Mathematician that expand on the topics treated in Chapter 1, and to solve their exercises. Other books, most notably Riehl's Category Theory in Context, are now often recommended as a first introduction to category theory. These have some improvements over Mac Lane, but it might be that the best preparation for Mac Lane-Moerdijk is Mac Lane himself. Either way should be fine. Turi's notes look nice but you want many more exercises.

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  • $\begingroup$ Ah, yes; it's in my copy too. Thank you :) $\endgroup$
    – Shaun
    Mar 11 '20 at 23:29

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