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The Swiss cheese operad is an analogue of the little disks operad, where disks are replaced by half-disks, which contain both ordinary disks in their interior, as well as half-disks positioned at the flat boundary.
This structure can be organized into an operad in the category of modules over the little disks operad.
Alexander Voronov, The Swiss-Cheese Operad, arXiv:math/9807037.
Najib Idrissi, Swiss-Cheese operad and Drinfeld center, arXiv:1507.06844.
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