The center of the Yoshida algebra of a finite groupoid is isomorphic to the center of its groupoid algebra, and the crossed Burnside ring of the groupoid surjects onto that center.
Brandt, \" U ber eine Verallgemeinerung des Gruppenbegriffes, Math
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Yoshida algebra for groupoids
The center of the Yoshida algebra of a finite groupoid is isomorphic to the center of its groupoid algebra, and the crossed Burnside ring of the groupoid surjects onto that center.