2014/07/28 by Kaoutit, Laiachi El, Kowalzig, Niels
#Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1407.7461
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.