  We prove that, for every extension of Banach algebras $ 0 \rightarrow B
\rightarrow A \rightarrow D \rightarrow 0 $ such that $B$ has a left or right
bounded approximate identity, the existence of an associated long exact
sequence of Banach simplicial or cyclic cohomology groups is equivalent to the
existence of one for homology groups. It follows from the continuous version of
a result of Wodzicki that associated long exact sequences exist. In particular,
they exist for every extension of $C^*$-algebras.
