Infra-nilmanifold endomorphisms were introduced in the late sixties. They
play a very crucial role in dynamics, especially when studying expanding maps
and Anosov diffeomorphisms. However, in this note we will explain that the two
main results in this area are based on a false result and that in fact these
two main theorems are not correct themselves! Moreover, we will also show that
the notion of an infra-nilmanifold endomorphism itself has not always been
interpreted in the same way. Finally, we define a slightly more general concept
of the notion of an infra-nilmanifold endomorphism and explain why this is
really the right concept to work with