Given a morphism \(\mathcal C\xrightarrow{F} \mathcal D\) in \(\mathrm{Cat}_{(\infty, {k})}\), we refer to its unique factorization28 guaranteed by the (\(n\)-surjective, \(n\)-faithful) factorization system as its \(n\)-factorization, and denote it by \[\mathrm{Fact}_n(F) \coloneqq \mathrm{Fact}_{\textup{($n$-surjective, $n$-faithful)}}(F) \in \mathrm{Cat}_{(\infty, {k})}.\]
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2