Approximations and locally free modules

Abstract

For any set of modules S, we prove the existence of precovers (right approximations) for all classes of modules of bounded C-resolution dimension, where C is the class of all S-filtered modules. In contrast, we use infinite dimensional tilting theory to show that the class of all locally free modules induced by a non-sum-pure-split tilting module is not precovering. Consequently, the class of all locally Baer modules is not precovering for any countable hereditary artin algebra of infinite representation type.

14 pages

References in corpus (2)

• On exact categories and applications to triangulated adjoints and model structures
• Deconstructibility and the Hill lemma in Grothendieck categories

Cited by in corpus (3)

• Flat relative Mittag-Leffler modules and approximations
• Resolutions as directed colimits
• Flat Mittag-Leffler modules, and their relative and restricted versions