  Stable equivalences of Morita type preserve many interesting properties and
is proved to be the appropriate concept to study for equivalences between
stable categories. Recently the singularity category attained much attraction
and Xiao-Wu Chen and Long-Gang Sun gave an appropriate definition of singular
equivalence of Morita type. We shall show that under some conditions singular
equivalences of Morita type have some biadjoint functor properties and preserve
positive degree Hochschild homology.
