Weak silting modules (Q6613020)

Tilting theory has been a very successful technique used both to pass informations from one algebra to another and to better understand internally a module category. It dates back to the 1980s. More recently, silting theory has been introduced as a generalization of tilting theory and it has been the object of much study in the representation theory of modules. In this paper, the authors study properties of the so-called weak \(n\)-silting modules. In particular, they look at the relations of such objects in terms of partial \(n\)-silting, weak \(n\)-tilting or partial \(n\)-tilting modules. Also, they extend to the context of weak \(n\)-silting modules a characterization of pure-injectivity for cotilting modules established by \textit{S. Bazzoni} [J. Algebra 273, No. 1, 359--372 (2004; Zbl 1051.16007)]. The authors provide in the introduction a short but very good account of how the mentioned theories were developed.