Endomorphism category monoidal

Theorem 19.4.6 ([Lurie (2017), Proposition 4.7.1.30, Theorem 4.7.1.34]). Let \(D\) be left-tensored over a monoidal \(\infty \)-category \(C\), and let \(M \in D\). The endomorphism category \(C[M]\) admits a monoidal structure for which the forgetful functor \(C[M] \to C\) is monoidal. Moreover, there is an equivalence \[ \Alg (C[M]) \iso \LMod (D) \times _D \{M\} \] compatible with the forgetful functors to \(\Alg (C)\).