2015/01/27 by Simion Breaz, Breaz, Simion, George-Ciprian Modoi +1
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #math.CT #math.RT
paper · pdf · doi:10.48550/arxiv.1501.06810
Comments are welcome; v2: some details and comments added, and a more conceptual proof for Salce's Lemma is presented; correction of several misprints in text (e.g. for the Toda bracket ideal associated to object ideals); v3: the paper is reorganized, some examples are added, and the references are updated
arxiv created 2017/07/01 · arxiv updated 2017/07/04
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.