Right adjoint oplax monoidal functor

Remark 14.3.7. In the previous proposition, it does not suffice for \(L\) to be a lax symmetric monoidal functor itself. It would suffice for \(L\) to be an oplax symmetric monoidal functor, but producing the lax symmetric monoidal right adjoint is more subtle in this case. Dually, the left adjoint to a lax symmetric monoidal functor is oplax symmetric monoidal. We refer to [Haugseng et al. (2023), Proposition A] for a detailed discussion.