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The Stacks project

Remark 13.19.5. Let \mathcal{A} be an abelian category. Suppose that \alpha : K^\bullet \to L^\bullet is a quasi-isomorphism of complexes. Let P^\bullet be a bounded above complex of projectives. Then

\mathop{\mathrm{Hom}}\nolimits _{K(\mathcal{A})}(P^\bullet , K^\bullet ) \longrightarrow \mathop{\mathrm{Hom}}\nolimits _{K(\mathcal{A})}(P^\bullet , L^\bullet )

is an isomorphism. This is dual to Remark 13.18.5.

Comments (2)

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View Remark 13.19.5 as pdf