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Ideal cotorsion theories in triangulated categories

Authors
  • Breaz, Simion
  • Modoi, George-Ciprian
Type
Preprint
Publication Date
Feb 24, 2015
Submission Date
Jan 27, 2015
Identifiers
arXiv ID: 1501.06810
Source
arXiv
License
Yellow
External links

Abstract

We study ideal cotorsion pairs associated to weak proper classes of triangles in extension closed subcategories of triangulated categories. This approach allows us to extend the recent ideal approximations theory developed by Fu, Herzog et al. for exact categories in the above mentioned context, and to provide simplified proofs for the ideal versions of some standard results as Salce's Lemma, Wakamatsu's Lemma and Christensen's Ghost Lemma. In the last part of the paper we apply the theory in order to study connections between projective classes (in particular localization or smashing subcategories) in compactly generated categories and cohomological functors into Grothendieck categories.

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