  We consider a possible framework to categorify the exponential map exp(-f)
given the categorification of a generator f of $\frak{sl}_2$ by Lauda. In this
setup the Taylor expansions of exp(-f) and exp(f) turn into complexes built out
of categorified divided powers of f. Hom spaces between tensor powers of
categorified f are given by diagrammatics combining nilHecke algebra relations
with those for a additional "short strand" generator. The proposed framework is
only an approximation to categorification of exponentiation, because the
functors categorifying exp(f) and exp(-f) are not invertible.
