Definition 13.23.2. Let \mathcal{A} be an abelian category with enough injectives. A resolution functor1 for \mathcal{A} is given by the following data:
for all K^\bullet \in \mathop{\mathrm{Ob}}\nolimits (K^{+}(\mathcal{A})) a bounded below complex of injectives j(K^\bullet ), and
for all K^\bullet \in \mathop{\mathrm{Ob}}\nolimits (K^{+}(\mathcal{A})) a quasi-isomorphism i_{K^\bullet } : K^\bullet \to j(K^\bullet ).
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