Splitting monoidal stable model categories

被引：13

作者：

Barnes, D. ^{[1
]}

机构：

[1] Max Planck Inst Math, D-53111 Bonn, Germany

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2009年 / 213卷 / 05期

关键词：

MODULES; SPECTRA;

D O I：

10.1016/j.jpaa.2008.10.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S, S](C). An idempotent e of this ring will split the homotopy category: [X, Y](C) congruent to e[X, Y](C) circle plus (1 - e) [X, Y](C). We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to L(eS)C x L((1-e)S)C and [X, Y](LeSC) congruent to e[X, Y](C). This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：846 / 856

页数：11