Abstract
Theorem 2.2 stated a monoidal isomorphism between the comodule categories of two bialgebroids in a Hopf algebroid. The proof of Theorem 2.2 was based on the journal version of Brzeziński (Ann Univ Ferrara Sez VII (NS) 51:15–27, 2005, Theorem 2.6), whose proof turned out to contain an unjustified step. Here we show that all other results in our paper remain valid if we drop unverified Theorem 2.2, and return to an earlier definition of a comodule of a Hopf algebroid that distinguishes between comodules of the two constituent bialgebroids.
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The online version of the original article can be found at http://dx.doi.org/10.1007/s10485-006-9043-6.
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Böhm, G., Brzeziński, T. Corrigendum to Cleft Extensions of Hopf Algebroids. Appl Categor Struct 17, 613–620 (2009). https://doi.org/10.1007/s10485-008-9168-x
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DOI: https://doi.org/10.1007/s10485-008-9168-x