I'm reading "categories for the working mathematician " of MacLane. At page 202, we define what is a morphism of short exact sequences (in an abelian category) and say that this form the category of short exact sequences. This category is additive. My question is : is this category abelian? First my intuition was "yes" but then I tried to prove it... Now I'm convinced that the answer is "No" because of some constructions we can not do with kernels. Any help? Any counterexample?
2026-03-26 12:13:37.1774527217
Do short exact sequences form an abelian category?
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