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It is the $\\mathfrak{sl}_3$ analogue of Khovanov's arc algebra.\n  We prove that $K^S$ is a graded symmetric Frobenius algebra. Furthermore, we categorify an instance of $q$-skew Howe duality, which allows us to prove that $K^S$ is Morita equivalent to a certain cyclotomic KLR-algebra of level 3. 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