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I am working on a homework problem for a class and found that the part I am stuck on can be reduced to the following: Let $u: M \to M'$ and $v: N \to N'$ be module homomorphisms. I am trying to understand the map $(u,v): \text{Hom}(M, N) \to \text{Hom}(M', N')$. My main question is: if $f \in \text{Hom}(M,N)$, how do I determine what $(u,v)(f)$ is?

My initial guess was that its a function that results in a commutative square but wasn't able to show that the function I had in mind was well-defined.

Yunus Syed
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    that should be just composition shouldn't it? also you messed up the direction of one arrow (Hom is contravariant in the first variable). I.e. to get $$\mathrm(Hom)(M,N) \to \mathrm(Hom)(M',N)$$ you need $u: M' \to M$. I would suggest you draw that as a small triangle on a piece of paper to wrap your mind around. – Felix Sep 06 '19 at 07:13
  • @Enkidu I found out the reason I was having difficulty was because this was a typo in both the textbook and homework assignment. I asked this question to my professor and he forgot to fix the typo. Thanks for your answer! – Yunus Syed Sep 06 '19 at 18:14

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