  Several papers have, as their raison d'etre, the exploration of the
\emph{generalized Lau product} associated to a homomorphism $T:B\to A$ of
Banach algebras. In this short note, we demonstrate that the generalized Lau
product is isomorphic as a Banach algebra to the usual direct product $A\oplus
B$. We also correct some misleading claims made about the relationship between
this generalized Lau product, and an older construction of Monfared (Studia
Mathematica, 2007).
