ScalingStacks

Given morphisms \(a \xrightarrow{l} b\) and \(c \xrightarrow{r} d\) in an \(\infty\)-category, we say that \(l\) is left orthogonal to \(r\) or that \(r\) is right orthogonal to \(l\) if for any solid commutative square the space of dashed lifts \(b \rightarrow c\) is contractible. In this situation, we may write \(l \bot r\). More broadly, given classes \(\mathcal L\) and \(\mathcal R\) of morphisms in an \(\infty\)-category, we write \(\mathcal L\bot \mathcal R\) to indicate that \(l \bot r\) for every \(l \in \mathcal L\) and every \(r \in \mathcal R\).