The Stacks project

Definition 12.27.1. Let $\mathcal{A}$ be an abelian category. An object $J \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A})$ is called injective if for every injection $A \hookrightarrow B$ and every morphism $A \to J$ there exists a morphism $B \to J$ making the following diagram commute

\[ \xymatrix{ A \ar[r] \ar[d] & B \ar@{-->}[ld] \\ J & } \]

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View Definition 12.27.1 as pdf