The Stacks project

Definition 21.44.1. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\mathcal{E}^\bullet$ be a complex of $\mathcal{O}$-modules. We say $\mathcal{E}^\bullet$ is strictly perfect if $\mathcal{E}^ i$ is zero for all but finitely many $i$ and $\mathcal{E}^ i$ is a direct summand of a finite free $\mathcal{O}$-module for all $i$.