A new approach to model categorical homotopy fiber sequences

IF 1.5 3区数学 Q1 MATHEMATICS

Dissertationes Mathematicae Pub Date : 2021-09-25 DOI:10.4064/dm858-5-2022

Alisa Govzmann, Damjan Pivstalo, N. Poncin

引用次数: 2

Abstract

We propose a simplified definition of Quillen’s fibration sequences in a pointed model category that fully captures the theory, although it is completely independent of the concept of action. This advantage arises from the understanding that the homotopy theory of the model category’s arrow category contains all homotopical information about its long fibration sequences. MSC 2020: 18E35, 18N40, 14A30

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分类同伦纤维序列模型的一种新方法

我们提出了一个简化的定义，Quillen的纤颤序列在一个点模型类别，充分捕捉理论，虽然它是完全独立于动作的概念。这种优势来自于模型范畴的箭头范畴的同伦理论包含了它的长颤振序列的所有同伦信息。MSC 2020: 18e35, 18n40, 14a30

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Dissertationes Mathematicae 数学-数学

CiteScore

2.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： DISSERTATIONES MATHEMATICAE publishes long research papers (preferably 50-100 pages) in any area of mathematics. An important feature of papers accepted for publication should be their utility for a broad readership of specialists in the domain. In particular, the papers should be to some reasonable extent self-contained. The paper version is considered as primary. The following criteria are taken into account in the reviewing procedure: correctness, mathematical level, mathematical novelty, utility for a broad readership of specialists in the domain, language and editorial aspects. The Editors have adopted appropriate procedures to avoid ghostwriting and guest authorship.