Definition 6.1.2. A 1-category \(\Aa \) is called an abelian category if it is additive, has kernels and cokernels, and a nullsequence \(A \xhookrightarrow {i} B \overset {p}{\twoheadrightarrow } C\) with \(i\) a monomorphism and \(p\) an epimorphism is a fiber sequence (i.e. \(A \iso \ker (p)\)) if and only if it is a cofiber sequence (i.e. \(\coker (i) \iso C\)). We will display such nullsequences as \[ 0 \to A \xhookrightarrow {i} B \overset {p}{\twoheadrightarrow } C \to 0, \] and refer to them as short exact sequences.
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