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MR2803849 (2012f:18018) 18D10 (17B10 20C20 57R56)
Geer, Nathan; Kujawa, Jonathan; Patureau-Mirand, Bertrand Generalized trace and modified dimension functions on ribbon categories. Selecta Math. (N.S.) 17 (2011), no. 2, 453–504.
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