I'm currently reading Theo Bühler's survey on exact categories about which he says
This article is written for the reader who wants to learn about exact categories and knows why. Very few motivating examples are given in this text
It turns out I don't really know any applications of homological algebra, so the article seems pretty dry to me. For example, every one seems to be very fond of diagram lemmas, but for the moment I see no interest in them. Is there any nice non-trivial theorem than can be proved with the tools developped in that text ? It would really help my reading become more pleasant.
EDIT: I'm very surprised to see that this question has not recieved any answer, or even any comments. I'm going to develop my question some more hoping that this changes.
While reading the article I always use the example of abelian groups. This helps me find interest in the article, since it gives a new (element free) perspective on familiar concepts, like the isomorphism theorems. However homological algebra seems to be a rather important theory, so I imagined there must be some theorem that can be formulated outside homological algebra and proved with its methods.
If this it not the case, then an answer saying so would perfectly answer my question. However I suspect this is not the case, since it seems homological algebra is connected to many areas of mathematics. If there are such theorems, but they require more heavy tools than those developed in the article, an answer explaining it would be very welcome.