Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathfrak{gl}_n$-webs, categorification and Khovanov-Rozansky
  homologies   In this paper we define an explicit basis for the $\mathfrak{gl}_n$-web
algebra $H_n(\vec{k})$ (the $\mathfrak{gl}_n$ generalization of Khovanov's arc
algebra) using categorified $q$-skew Howe duality.
  Our construction is a $\mathfrak{gl}_n$-web version of Hu--Mathas' graded
cellular basis and has two major applications: it gives rise to an explicit
isomorphism between a certain idempotent truncation of a thick calculus
cyclotomic KLR algebra and $H_n(\vec{k})$, and it gives an explicit graded
cellular basis of the $2$-hom space between two $\mathfrak{gl}_n$-webs. We use
this to give a (in principle) computable version of colored Khovanov-Rozansky
$\mathfrak{gl}_n$-link homology, obtained from a complex defined purely
combinatorially via the (thick cyclotomic) KLR algebra and needs only $F$.

1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int