Let \(\mathcal K\) be a small set of simplicial sets, \(\mathbb V\in \mathrm{Alg}(\mathrm{Cat}_{\infty}^{\mathcal K})\) and \(\mathcal C, \mathcal D\in \mathrm{LMod}_{\mathbb V}(\mathrm{Cat}_{\infty}^{\mathcal K})\). Let \(\mathrm{Fun}_{\mathbb V}(\mathcal C, \mathcal D)\) be the \(\infty\)-category of \(\mathbb V\)-module functors [Lur17, Def. 4.6.2.7] and \(\mathrm{Fun}^{\mathcal K}_{\mathbb V}(\mathcal C, \mathcal D) \subset \mathrm{Fun}_{\mathbb V}(\mathcal C, \mathcal D)\) the full subcategory on those module functors whose underlying functors preserve \(\mathcal K\)-colimits.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2