Flat covers in abelian and in non-abelian categories

被引：16

作者：

Rump, Wolfgang ^{[1
]}

机构：

[1] Univ Stuttgart, Inst Algebra & Number Theory, D-70550 Stuttgart, Germany

来源：

ADVANCES IN MATHEMATICS | 2010年 / 225卷 / 03期

关键词：

Flat cover; Pure exact sequence; Left exact category; Locally finitely presented; Quasi-abelian; Grothendieck category; Ramsey theory; ENVELOPES; COMPLEXES;

D O I：

10.1016/j.aim.2010.03.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A general existence theorem for flat covers in (e.g., quasi-abelian) locally finitely presented categories is obtained from an additive Ramsey type theorem. In the abelian case, it is shown that flat covers always exist. Applications to categories of separated presheaves or sheaves, localizations of Bousfield type, torsion-free classes of finite type, and categories of filtered objects or complexes, are given. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1589 / 1615

页数：27

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