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In mathematics, a quantum groupoid is any of a number of notions in noncommutative geometry analogous to the notion of groupoid. In usual geometry, the information of a groupoid can be contained in its monoidal category of representations , in its groupoid algebra or in the commutative Hopf algebroid of functions on the groupoid. Thus formalisms trying to capture quantum groupoids include certain classes of monoidal categories, Hopf algebroids etc.
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