Liftable pairs of functors and Initial objects

Alessandro Ardizzoni, Isar Goyvaerts, Claudia Menini

Let $\mathcal{A}$ and $\mathcal{B}$ be monoidal categories and let $R:\mathcal{A}\to \mathcal{B}$ be a lax monoidal functor. If $R$ has a left adjoint $L$, it is well-know…