Cosilting Modules

TL;DR

This paper introduces cosilting modules, explores their properties and relationships with silting modules, and extends Bazzoni's pure-injectivity theorem from cotilting to cosilting modules.

Contribution

It provides new characterizations of cosilting modules and establishes their connection with silting modules, extending existing theorems to this dual class.

Findings

Cosilting modules are characterized and related to silting modules.

Bazzoni's pure-injectivity theorem is extended to cosilting modules.

The paper establishes foundational properties of cosilting modules.

Abstract

We study the class of modules, called cosilting modules, which are defined as the categorical duals of silting module. Several characterizations of these modules and connections with silting modules are presented. We prove that Bazzoni theorem about the pure-injectivity of cotilting modules is also valid for cosilting modules.