  For a Coxeter system and a representation $V$ of this Coxeter system, Soergel
defined a category which is now called the category of Soergel bimodules and
proved that this gives a categorification of the Hecke algebra when $V$ is
reflection faithful. Elias and Williamson defined another category even when
$V$ is not reflection faithful and they proved that this category is equivalent
to the category of Soergel bimodules when $V$ is reflection faithful. Moreover
they proved the categorification theorem for their category with less
assumptions on $V$. In this paper, we give a "bimodule theoretic" definition of
the category of Elias-Williamson and reprove the categorification theorem.
