The extensions of t-structures

TL;DR

This paper revisits Keller's result on extending t-structures, providing a detailed proof and exploring concepts like regular t-structures and global dimensions in hereditary contexts.

Contribution

It offers a detailed proof of Keller's result and discusses the roles of regular t-structures and global dimensions in hereditary cases.

Findings

Reformulation of Keller's extension result for t-structures

Introduction of regular t-structures in hereditary settings

Analysis of global dimensions related to t-structures

Abstract

We reformulate a result of Bernhard Keller on extensions of $t$-structures and give a detailed proof. In the study of hereditary $t$-structures, the notions of regular $t$-structures and global dimensions arise naturally.