On purely generated α-smashing weight structures and weight-exact localizations

JOURNAL OF ALGEBRA

卷:535

Article

关键词: Triangulated categories;    Weight structures;    Weight-exact functors;    Localizations;    alpha-smashing classes;    Localizing subcategories;    Compact objects;    Stable homotopy category;    Generalized universal localizations of rings;    Perfect classes;   

DOI  :  10.1016/j.jalgebra.2019.07.003

来源: Elsevier

【 摘 要 】

This paper is dedicated to new methods of constructing weight structures and weight-exact localizations; our arguments generalize their bounded versions considered in previous papers of the authors. We start from a class of objects P of a triangulated category (C) under bar that satisfies a certain (countable) negativity condition (there are no (C) under bar -extensions of positive degrees between elements of P; we actually need a somewhat stronger condition of this sort) to obtain a weight structure both halves of which are closed either with respect to (C) under bar -coproducts of less than a objects (where alpha is a fixed regular cardinal) or with respect to all coproducts (provided that (C) under bar is closed with respect to coproducts of this sort). This construction gives all reasonable weight structures satisfying the latter conditions. In particular, one can obtain certain weight structures on spectra (in SH) consisting of less than a cells, and on certain localizations of SH; these results are new. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free