The t-structures generated by objects

TL;DR

This paper proves the existence of t-structures generated by arbitrary sets of objects in well generated triangulated categories, extending a previous result that required additional assumptions on the category.

Contribution

It generalizes a 2003 theorem by removing the need for the category to have a specific model, broadening the applicability of t-structure generation.

Findings

Existence of t-structures for any set of objects in well generated categories

Extension of previous results without model assumptions

Facilitates study of t-structures generated by arbitrary objects

Abstract

Let $\mathcal T$ be a well generated triangulated category, and let $S\subset\mathcal T$ be a set of objects. We prove that there is a t-structure on $\mathcal T$ with ${\mathcal T}^{\leq0}=\overline{\langle S\rangle}^{(-\infty,0]}$. This article is an improvement on the main result of a 2003 article by Alonso, Jeremias and Souto---in that article the theorem was proved under the assumption that $\mathcal T$ has a nice enough model. It should be mentioned that the theorem of Alonso, Jeremias and Souto has been influential---it turns out to be interesting to study all of these t-structures.