$2$-category of Soergel bimodules is roughly captured by the Kazhdan-Lusztig combinatorics of the so-called [*two-sided Kazhdan-Lusztig cells*]{}. The minimal, with respect to the two-sided order, two-sided cell corresponds to the identity element. If we take this minimal two-sided cell out, in what remains there is again a unique minimal two-sided cell. This is the two-sided cell which contains all simple reflections. The main object of study in the present paper is the unique “simple” quotient of the $2$-category of Soergel bimodules in which only these two smallest two-sided cells survive. This is the $2$-category which we call the [*small quotient*]{} of the $2$-category of Soergel bimodules. Our main result is the following statement that combines the statements of Theorems \[thm1700\], \[thm49\], \[thm82\], \[thm84\], \[thm86\] and \[thm88\].

\[thmintro\] Let $\underline{{\sc\mbox{S}\hspace{1.0pt}}}$ be the small quotient of the $2$-category of Soergel bimodules over the coinvariant algebra associated to a finite Coxeter system $(W,S)$.

1.  \[thmintro.1\] If $W$ has rank greater than two or is of Coxeter type $I_2(n)$, with $n=4$ or $n>1$ odd, then every simple transitive $2$-representation of $\underline{{\sc\mbox{S}\hspace{1.0pt}}}$ is equivalent to a cell $2$-representation.

2.  \[thmintro.2\] If $W$ is of Coxeter type $I_2(n)$, with $n>4$ even, then, apart from cell $2$-representations, 