The (surjective-on-objects-and-dominant-on-1-morphisms, faithful)-functors define factorization systems on \(\mathrm{Cat}[\mathrm{add}_{k}^{B\mathbb{Z}}]\) and \(\mathrm{Alg}_{\mathbb E_1}(\mathrm{Cat}[\mathrm{add}_{k}^{B\mathbb{Z}}])\), respectively, which are of small generation and compatible with the symmetric monoidal structure.
Proof.
This follows immediately from applying theorem B.4.1 and then theorem B.3.1 to the factorization system of proposition 6.2.2. ◻
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2