Relative tensor products of \(\infty\)-categories of local systems

The Lurie tensor product is part of a symmetric monoidal structure on the \(\infty\)-category \(\mathrm{Pr}^\mathrm{L}\) of presentable \(\infty\)-categories.

It enjoys many good formal properties, and is often computable. An example of this computability is that if \(C\) is a small \(\infty\)-category and \(\mathcal{D,E}\) are presentable, then \(\mathcal D^C \otimes \mathcal E \simeq (\mathcal D\otimes \mathcal E)^C\). A special case of this is …