Tannaka-Krein duality for Hopf algebroids
For a ring \(R\), this paper uses the notion of \(R\)-coalgebroid defined by \textit{M. Takeuchi} [``\(\sqrt{\text{Morita}}\) theory: Formal ring laws and monoidal equivalences of categories of bimodules'', J. Math. Soc. Japan 39, 301--336 (1987; Zbl 0619.16032)] which have a counit and comultiplication on an underlying double \(R\)-bimodule. An \(R\)-bialgebroid is then a monoid in the monoidal category of \(R\)-coalgebroids; it is a Hopf algebroid when its category of finitely generated projective comodules is autonomous (rigid, compact). The paper develops Tannaka-Krein duality for Hopf algebroids and strong monoidal functors into the category of dual \(R\)-bimodules.
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