  We review (non-abelian) extensions of a given Lie algebra, identify a
3-dimensional cohomological obstruction to the existence of extensions. A
striking analogy to the setting of covariant exterior derivatives, curvature,
and the Bianchi identity in differential geometry is spelled out. In the new
version references added: Most of the results are known. So this paper will not
be submitted to a journal, it can be regarded as a review paper.
