Ingalls and Thomas introduced a construction relating torsion pairs and wide subcategories in the context of finite-dimensional modules over hereditary algebras. Their work was later generalized by Marks and Stovicek to arbitrary algebras. We apply this construction to cosilting torsion pairs in the category of all modules and give a description of the resulting wide subcategories as some generalized perpendicular categories. We show that all the wide subcategories we obtain are coreflective and discuss the case in which they are bireflective. We conclude with an application to the study of torsion pairs in the category of finite-dimensional modules. This is joint work with Lidia Angeleri.