Morita theory for Hopf algebroids, principal bibundles, and weak equivalences
L El Kaoutit, N Kowalzig - Documenta Mathematica, 2017 - ems.press
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 …
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 …
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