Morita Theory for Hopf Algebroids, Principal Bibundles, and Weak Equivalences
Morita Theory for Hopf Algebroids, Principal Bibundles, and Weak Equivalences
复制标题
Hopf 代数体、主双束和弱等价的 Morita 理论
作者：
L. Kaoutit;N. Kowalzig
我们证明了两个平坦交换的Hopf代数胚是Morita等价的当且仅当它们是弱等价的，并且当且仅当存在一个主双丛连接它们。这给出了一个肯定的答案猜想由于霍维和思特里克兰德。我们还证明了主（左）丛导致一个bicategory连同一个2函子从平坦的Hopf代数胚平凡的主丛。这证明是2-函子的普遍解决方案，它发送弱等价到可逆的1-细胞。我们的方法可以看作是李群胚森田理论的代数对应。
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.