Bialgebroids, ×A-bialgebras and duality
Abstract
An equivalence between Lu's bialgebroids, Xu's bialgebroids with an anchor and Takeuchi's ×A-bialgebras is explicitly proven. A new class of examples of bialgebroids is constructed. A (formal) dual of a bialgebroid, termed bicoalgebroid, is defined. A weak Hopf algebra is shown to be an example of such a bicoalgebroid.
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