  We define and study categories of singular Soergel bimodules, which are
certain natural generalisations of Soergel bimodules. Indecomposable singular
Soergel bimodules are classified, and we conclude that the split Grothendieck
group of the 2-category of singular Soergel bimodules is isomorphic to the
Schur algebroid. Soergel's conjecture on the characters of indecomposable
Soergel bimodules in characteristic zero is shown to imply a similar conjecture
for the characters of singular Soergel bimodules.
