Justified by Observation B.1.10, given a morphism \(c \xrightarrow{f} d\) in an \(\infty\)-category \(\mathcal C\) equipped with a factorization system \((\mathcal L,\mathcal R)\), we write \(\mathrm{Fact}(f) \coloneqq \mathrm{Fact}_{(\mathcal L,\mathcal R)}(f) \in \mathcal C\) for the unique object through which \(f\) factors via the factorization system.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2