It follows from [Lur17, Prop. 4.8.1.17, Prop. 4.8.1.16] after taking adjoints, that the tensor product of presentable \(\infty\)-categories can be expressed as the following functor category (which is in particular presentable): \[ \mathcal C\otimes \mathcal D\simeq \mathrm{Fun^L}(\mathcal D, \mathcal C^\mathrm{op})^\mathrm{op}= \mathrm{Fun^R}(\mathcal C^\mathrm{op}, \mathcal D)\]
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2