
TL;DR
This paper introduces a method to construct exact commutative algebras in the center of a finite tensor category, using relative (co)ends to measure subcategory inclusions, with explicit examples.
Contribution
It develops a new approach to produce exact commutative algebras in the center of tensor categories via relative (co)ends, extending previous methods.
Findings
Explicit computations of the constructed algebras.
A new categorical tool for measuring subcategory inclusions.
Extension of Shimizu's construction using relative (co)ends.
Abstract
Given a finite tensor category , an exact indecomposable -module category , and a tensor subcategory , we describe a way to produce \textit{exact} commutative algebras in the center , 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra
