83 research outputs found
Morita theory for Hopf algebroids, principal bibundles, and weak equivalences
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.Comment: 50 pages; v2: added a section in which we exhibit the categorical
group structure of monoidal symmetric autoequivalences. v3: added a section
which explains the abstract groupoid case as a guideline and for motivation.
To appear in Doc. Mat
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