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arXiv · 1210.8052

The uniqueness of braidings on the monoidal category of non-commutative descent data

A. L. Agore·S. Caenepeel·G. Militaru
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Abstract

Let $A$ be an algebra over a commutative ring $k$. It is known that the categories of non-commutative descent data, of comodules over the Sweedler canonical coring, of right $A$-modules with a flat connection are isomorphic as braided monoidal categories to the center of the category of $A$-bimodules. We prove that the braiding on these categories is unique if there exists a $k$-linear unitary map $E : A \to Z(A)$. This condition is satisfied if $k$ is a field or $A$ is a commutative or a separable algebra.

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A. L. Agore, S. Caenepeel, G. Militaru. 2012-10-30. The uniqueness of braidings on the monoidal category of non-commutative descent data. https://arxiv.org/abs/1210.8052

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