Gluing n-tilting and n-cotilting subcategories

TL;DR

This paper explores how n-tilting and n-cotilting subcategories can be combined within extriangulated categories using recollement structures, extending known concepts from abelian and triangulated categories.

Contribution

It demonstrates that n-tilting and n-cotilting subcategories can be glued in extriangulated categories via recollement, generalizing previous results.

Findings

n-tilting and n-cotilting subcategories can be glued in extriangulated categories

The paper extends the concept of recollement to extriangulated categories

Conditions are identified under which tilting subcategories can be combined

Abstract

Recently, Wang, Wei and Zhang define the recollement of extriangulated categories, which is a generalization of both recollement of abelian categories and recollement of triangulated categories. For a recollement $(\mathcal A ,\mathcal B,\mathcal C)$ of extriangulated categories, we show that $n$-tilting (resp. $n$-cotilting) subcategories in $\mathcal A$ and $\mathcal C$ can be glued to get $n$-tilting (resp. $n$-cotilting) subcategories in $\mathcal B$ under certain conditions.