Given a finite tensor category \({\cal C}\) , an exact indecomposable \({\cal C}\) -module category \({\cal M}\) , and a tensor subcategory \({\cal D} \subseteq {\cal C}_{\cal M}^{\ast}\) , we describe a way to produce exact commutative algebras in the center \(Z({\cal C})\) , measuring this inclusion. The construction of such algebras is done in an analogous way as presented by Shimizu [20], but using instead the relative (co)end, a categorical tool developed in [1] in the realm of representations of tensor categories. We provide some explicit computations.
