Resumen

In the research field of higher homological algebra, distinguished sequences with d middle terms play a fundamental role. In the case d = 1, one recovers the short exact sequences and distinguished triangles of abelian and triangulated categories, and the theory corresponds to classical homological algebra. We discuss the notion of a torsion class in the higher-dimensional setup. We give a characterisation of higher torsion classes, demonstrating that the higher notion aligns well with classical theory. Time permitting, we moreover discuss how to extend classical results relating functorially finite torsion classes to tau-tilting pairs and silting complexes.
The talk is based on joint work with Jenny August, Karin M. Jacobsen, Sondre Kvamme, Yann Palu and Hipoloto Treffinger.