ScalingStacks

Definition B.1.15.

In the context of Proposition B.1.14, we say that the factorization system \((\mathcal L,\mathcal R)\) (or simply the left class \(\mathcal L\)) is of small generation, or more specifically that it is generated by \(S\). Moreover, we may write \(\overline{S}\) for \(\mathcal L\). We define the subcategories \[{\Pr}^{L,\text{f.s.},\mathcal L} \subset \widehat{\mathrm{Cat}}_\infty^{\text{f.s.},\mathcal L} \qquad \text{and} \qquad {\Pr}^{R,\text{f.s.},\mathcal R} \subset \widehat{\mathrm{Cat}}_\infty^{\text{f.s.},\mathcal R}\] to be those on the presentable \(\infty\)-categories whose factorization systems are of small generation, whose morphisms are respectively required to be left or right adjoints (in addition to preserving the indicated class of the factorization system).