Mackaay, MarcoYonezawa, Yasuyoshi2020-07-242020-07-242019-050022-40491873-1376http://hdl.handle.net/10400.1/14364In this paper we show how the colored Khovanov-Rozansky Sl(N)-matrix factorizations, due to Wu [45] and Y.Y. [46,47], can be used to categorify the type A quantum skew Howe duality defined by Cautis, Kamnitzer and Morrison in [14]. In particular, we define Sl(N)-web categories and 2-representations of Khovanov and Lauda's categorical quantum sl(m) on them. We also show that this implies that each such web category is equivalent to the category of finite-dimensional graded projective modules over a certain type A cyclotomic KLR-algebra. (C) 2018 Elsevier B.V. All rights reserved.engHighest weight categoriesKnot homologyCoherent sheavesjournal article10.1016/j.jpaa.2018.07.013