Formula omitted]-web categories and categorified skew Howe duality

Abstract

In this paper we show how the colored Khovanov–Rozansky slN-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 slN-web categories and 2-representations of Khovanov and Lauda's categorical quantum slm 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.