The Stacks project

Definition 64.10.1. We denote by $K_{perf}(\Lambda )$ the category whose objects are bounded complexes of finite projective $\Lambda$-modules, and whose morphisms are morphisms of complexes up to homotopy. The functor $K_{perf}(\Lambda )\to D(\Lambda )$ is fully faithful (Derived Categories, Lemma 13.19.8). Denote $D_{perf}(\Lambda )$ its essential image. An object of $D(\Lambda )$ is called perfect if it is in $D_{perf}(\Lambda )$.