Terminology 5.3.
Recall from Proposition A.3 that the morphisms in \(R\) are precisely those that are right orthogonal to the morphisms in \(L\). In particular, a modality is completely determined by the class \(L\). In what follows, we may sometimes refer to a class of morphisms \(L\) as a modality if the pair \((L,L^{\perp})\) is a modality.