  We equip Ellis and Brundan's version of the odd categorified quantum group
for sl(2) with a differential giving it the structure of a graded
dg-2-supercategory. The presence of the super grading gives rise to two
possible decategorifications of the associated dg-2-category. One version gives
rise to a categorification of quantum sl(2) at a fourth root of unity, while
the other version produces a subalgebra of quantum gl(1|1) defined over the
integers. Both of these algebras appear in connection with quantum algebraic
approaches to the Alexander polynomial.
