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arXiv · 1407.7461

Morita theory for Hopf algebroids, principal bibundles, and weak equivalences

Laiachi El Kaoutit·Niels Kowalzig
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Abstract

We show that two flat commutative Hopf algebroids are Morita equivalent if and only if they are weakly equivalent and if and only if there exists a principal bibundle connecting them. This gives a positive answer to a conjecture due to Hovey and Strickland. We also prove that principal (left) bundles lead to a bicategory together with a 2-functor from flat Hopf algebroids to trivial principal bundles. This turns out to be the universal solution for 2-functors which send weak equivalences to invertible 1-cells. Our approach can be seen as an algebraic counterpart to Lie groupoid Morita theory.

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BibTeXRIS

Laiachi El Kaoutit, Niels Kowalzig. 2014-07-28. Morita theory for Hopf algebroids, principal bibundles, and weak equivalences. https://arxiv.org/abs/1407.7461

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