The Stacks project

Definition 13.14.9. In Situation 13.14.1. We say $F$ is right derivable, or that $RF$ everywhere defined if $RF$ is defined at every object of $\mathcal{D}$. We say $F$ is left derivable, or that $LF$ everywhere defined if $LF$ is defined at every object of $\mathcal{D}$.