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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