Extending (τ-)tilting subcategories and (co)silting modules

Assume that B is a finite dimensional algebra, and A=B[P-0] is the one-point extension algebra of B using a finitely generated projective B-module P-0. The categories of B-modules and A-modules are connected via two adjoint functors known as the restriction and extension functors, denoted by R and epsilon, respectively. These functors have nice homological properties and have been studied in the category mod-A of finitely presented modules that we extend to the category Mod-A of all A-modules. Our main focus is to investigate the behavior of important subcategories (tilting and tau-tilting subcategories) and objects (finendo quasi-tilting modules, silting modules, and cosilting modules) under these functors.