Cotorsion pairs and a K-theory localization theorem

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Sarazola, Maru¹ 

[1] Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA

关键词: Cotorsion pair;    Exact category;    Waldhausen category;    Algebraic K-theory;    Localization;   

DOI  :  10.1016/j.jpaa.2020.106399

来源: Elsevier

【 摘 要 】

We show that a complete hereditary cotorsion pair (C, C-perpendicular to) in an exact category epsilon, together with a subcategory Z subset of epsilon containing C-perpendicular to, determines a Waldhausen category structure on the exact category C, in which Z is the class of acyclic objects. This allows us to prove a new version of Quillen's Localization Theorem, relating the K-theory of exact categories A subset of B to that of a cofiber. The novel idea in our approach is that, instead of looking for an exact quotient category that serves as the cofiber, we produce a Waldhausen category, constructed through a cotorsion pair. Notably, we do not require A to be a Serre subcategory, which produces new examples. Due to the algebraic nature of our Waldhausen categories, we are able to recover a version of Quillen's Resolution Theorem, now in a more homotopical setting that allows for weak equivalences. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free