  We define Lie 3-algebras and prove that these are in 1-to-1 correspondence
with the 3-term Lie infinity algebras whose bilinear and trilinear maps vanish
in degree (1,1) and in total degree 1, respectively. Further, we give an answer
to a question of [Roy07] pertaining to the use of the nerve and normalization
functors in the study of the relationship between categorified algebras and
truncated sh algebras.
