Singular Equivalence of Morita Type with Level

TL;DR

This paper introduces a new concept called singular equivalence of Morita type with level, which generalizes stable equivalence of Morita type and relates to singular categories and derived equivalences.

Contribution

It defines the notion of singular equivalence of Morita type with level and proves its relation to derived equivalences of standard type.

Findings

Singular equivalence of Morita type with level induces an equivalence between singular categories.

Derived equivalences of standard type induce singular equivalences of Morita type with level.

The new notion generalizes stable equivalence of Morita type.

Abstract

We generalize the notion of stable equivalence of Morita type and define what is called "singular equivalence of Morita type with level". Such an equivalence of induces an equivalence between singular categories. We will also prove that a derived equivalence of standard type induces a singular equivalence of Morita type with level.