A comparison between SLn spider categories
Abstract
We prove a conjecture of L\e and Sikora by providing a comparison between various existing SLn skein theories. While doing so, we show that the full subcategory of the spider category, Sp(SLn), defined by Cautis-Kamnitzer-Morrison, whose objects are monoidally generated by the standard representation and its dual, is equivalent as a spherical braided category to Sikora's quotient category. This also answers a question from Morrison's Ph.D. thesis. Finally, we show that the skein modules associated to the CKM and Sikora's webs are isomorphic.
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