Lemma 15.111.3. Let $R$ be a ring. Let $a^\bullet : K^\bullet \to L^\bullet $ and $b^\bullet : L^\bullet \to M^\bullet $ be maps of complexes of $R$-modules satisfying (1), (2), (3) above. Then we have $\det (a^\bullet ) \circ \det (b^\bullet ) = \det (b^\bullet \circ a^\bullet )$ as maps $\det (M^\bullet ) \to \det (K^\bullet )$.
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