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    Requirements for Hom(-,A) to be exact.

    I'm reading Algebra (GTM) by Serge Lang and I'm a bit confused about the requirements of theorem 6.3 in chapter 4 (Modules). Not the technical nature of them, but rather the motivation behind them so let me first present my take on the theorem. The theorem reads (text in square brackets are my...
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    Why is Nat(hom(A,-),F) a class?

    I'm trying to read a bit up on category theory, but I'm a bit confused about one aspect of the proof of Yoneda's lemma. Suppose we have a locally small category C, a functor F : C \to \textrm{Set} and an object A in C. Now according to Yoneda's lemma there exists a bijection from Nat(hom(A,-),F)...
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    Courses Skipping basic courses for advanced ones

    I'm about to start my first year of studying mathematics. My university requires me to take quite a lot of basic courses in the first year and after that there are some strict limits on the number of courses I can take. This means that I will not be able to take all the courses I would like to...
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