⁸lMany of the constructs in homological algebra regarding modules involve families of modules. And the theorems are of the same. Hence, I am a bit confused, how would this be helpful in understanding a particular module? Or are families of modules interesting for some in their right? In that case, could someone explain why?
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If you have one module and are solving a linear homogeneous equation in it, or a system, the set of solutions is a submodule. So, now you already have two modules to study. – plop Jan 05 '23 at 21:32
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It's times like this I wish I had the option to not gold-badge the duplicate mark. I think the title question is certainly a duplicate as linked, but maybe the body of the post makes it distinct (and it wouldn't look like a dupe after the title is revised.). I won't be sad if it's reopened along those lines. – rschwieb Jan 05 '23 at 21:35