Abstract
Assume that B is a finite dimensional algebra, and is the one-point extension algebra of B using a finitely generated projective B-module P0. The categories of B-modules and A-modules are connected via two adjoint functors known as the restriction and extension functors, denoted by
and
, respectively. These functors have nice homological properties and have been studied in the category
of finitely presented modules that we extend to the category
of all A-modules. Our main focus is to investigate the behavior of important subcategories (tilting and τ-tilting subcategories) and objects (finendo quasi-tilting modules, silting modules, and cosilting modules) under these functors.
Acknowledgments
We would like to thank the referee for her/his insightful comments and hints that improved the presentation of the paper. We also thank Lidia Angeleri Hügel for pointing out the reference [Citation10]. This work was partly done during a visit of the first author to the Institut des Hautes Études Scientifiques (IHES), Paris, France. The first and fourth authors would like to express their gratitude for the support and excellent atmosphere provided at IHES.