$\xi$-tilting objects in extriangulated categories

TL;DR

This paper introduces and studies the concept of $\xi$-tilting objects within extriangulated categories, extending existing results by generalizing the notion of tilting objects through a proper class of $ ext{E}$-triangles.

Contribution

It defines $\xi$-tilting objects in extriangulated categories, broadening the framework and extending prior results in the field.

Findings

Defined $\xi$-tilting objects in extriangulated categories

Extended results from previous work to a more general setting

Provided foundational properties and examples of $\xi$-tilting objects

Abstract

Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. In this article, we introduce and study the notion of $\xi$-tilting object in an extriangulated category, where $\xi$ is a proper class of $\mathbb{E}$-triangles. This extends results in \cite{YGH_2020}.