On singular equivalences of Morita type

TL;DR

This paper explores singular equivalences of Morita type, showing they have biadjoint functor properties and preserve positive degree Hochschild homology, thus advancing the understanding of stable and singularity categories.

Contribution

It demonstrates that under certain conditions, singular equivalences of Morita type possess biadjoint functor properties and preserve Hochschild homology, extending previous theoretical frameworks.

Findings

Singular equivalences of Morita type have biadjoint functor properties.

They preserve positive degree Hochschild homology.

The results deepen the understanding of stable and singularity categories.

Abstract

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.