Pospisil and J. Šťovíček to obtain a complete classification of compactly generated torsion pairs.
author:
- 'Mikhail V. Bondarko [^1]'
title: 'On torsion pairs, (well generated) weight structures, adjacent $t$-structures, and related (co)homological functors'
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[***2010 Mathematics Subject Classification.*** Primary 18E30 18E40 18G25; Secondary 14F05 55P42.]{}

[***Key words and phrases*** Triangulated category, torsion pair, weight structure, $t$-structure, adjacent structure, cohomological functor, pure functor, virtual $t$-truncation, compact object, perfect class, symmetric classes, Brown-Comenetz duality, well generated category, derived category of coherent sheaves, duality, pro-objects, projective class.]{}

Introduction {#introduction .unnumbered}
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The main goal of the current paper is to demonstrate the utility of weight structures to the construction and study of $t$-structures and of (co)homological functors from triangulated categories (into abelian ones). In particular, for a weight structure $w$ we study [*$w$-pure functors*]{} (i.e., those that “only see $w$-weight zero”).[^2]  Functors of this type have already found interesting applications in several papers (note in particular that the results of our §\[sdetect\] are important for the study of Picard groups of triangulated categories in [@bontabu]). So the author believes that the reader not interested in the construction weight structures and $t$-structures (that we will start discussing very soon) may still benefit from 