TL;DR
This paper introduces a construction linking algebras in monoidal categories to commutative algebras in their centers, demonstrating Morita invariance and applying it to group-theoretical categories.
Contribution
It extends the full centre construction to module categories and proves its Morita invariance, with applications to algebraic structures in conformal field theory.
Findings
The full centre construction is Morita invariant.
The construction applies to group-theoretical categories.
Provides a new perspective on algebraic structures in monoidal categories.
Abstract
Motivated by algebraic structures appearing in Rational Conformal Field Theory we study a construction associating to an algebra in a monoidal category a commutative algebra ({\em full centre}) in the monoidal centre of the monoidal category. We establish Morita invariance of this construction by extending it to module categories. As an example we treat the case of group-theoretical categories.
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