Given a finite tensor category $\ca$, an exact indecomposable $\ca$-module category $\Mo$, and a tensor subcategory $\Do\subseteq \ca^*_\Mo$, we describe a way to produce \textit{ exact} commutative algebras in the center $Z(\ca)$, measuring this inclusion. The construction of such algebras is done in an analogous way as presented by Shimizu \cite{ Sh2}, but using instead the \textit{ relative (co)end}, a categorical tool developed in \cite{ BM} in the realm of representations of tensor categories. We provide some explicit computations.
Categories: math.QA math.CT