J. Pure Appl. Algebra 214 (2010), no. 12, 2265-2278.
I find a presentation of Soergel category (as a tensor category) by generators and relations in the right-angled Coxeter group case. This problem was solved in complete generality in the beautiful paper Soergel calculus. In simple words, this could be summarized as “how to draw Soergel bimodules”.
PDF Presentation of right-angled Soergel categories by generators and relations