The homotopy categorical crossed module of a CW-complex

P. Carrasco; A.M. Cegarra; A.R. Garzon

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The homotopy categorical crossed module of a CW-complex

机译：CW复合体的同伦分类交叉模块

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摘要

Crossed modules have longstanding uses in homotopy theory and the cohomology of groups. The corresponding notion in the setting of categorical groups, that is, categorical crosses modules, allowed the development of a low-dimensional categorical group cohomology. Now, its relevance is also shown here to homotopy types by associating, to any pointed CW-complex (X, *), a categorical crossed module that algebraically represents the homotopy 3-type of X.

机译：交叉模块在同伦理论和群的同调学中有着长期的应用。分类组设置中的相应概念（即分类交叉模块）允许开发低维分类组同调。现在，通过将与任何尖的CW复数（X，*）相关联的代数交叉模块（代数表示X的同型3型）关联到同型类型，也显示了其相关性。

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来源
《Topology and its applications》 |2007年第4期|p.834-847|共14页
作者
P. Carrasco; A.M. Cegarra; A.R. Garzon;
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作者单位

Departamento de Algebra, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain;

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原文格式 PDF
正文语种 eng
中图分类高等数学;
关键词
categorical group; crossed module; cubical set; ω-groupoid; homotopy type;

机译：分类群;交叉模块;立方集;ω-类群;同伦型;

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专利

1. On the homotopy type and the fundamental crossed complex of the skeletal filtration of a CW-complex [J] . Jo?o Faria Martins Homology, Homotopy and Applications . 2007,第1期

机译：关于CW复合体骨骼过滤的同型和基本交叉复合体
2. Pointed homotopy and pointed lax homotopy of 2-crossed module maps [J] . Gohla B., Faria Martins J. Advances in Mathematics . 2013,第Null期

机译：2交叉模块图的尖同伦和尖松弛同伦
3. Categorical G-crossed modules and 2-fold extensions [J] . Carrasco P., Moreno JM. Journal of pure and applied algebra . 2001,第3期

机译：分类的G交叉模块和2倍扩展
4. Robust Multi-Class Classification Using Linearly Scored Categorical Cross-Entropy [C] . Chien-Hua Chen, Po-Hsiang Lin, Jer-Guang Hsieh, IEEE International Conference on Knowledge Innovation and Invention . 2020

机译：使用线性得分的分类交叉熵鲁棒多级分类
5. The homotopy theory of modules of curved A∞-algebras [D] . Armstrong, Jeffrey 2015

机译：弯曲A∞代数模块的同伦理论
6. Cross-species de novo identification of cis-regulatory modules with GibbsModule: Application to gene regulation in embryonic stem cells [O] . Dan Xie, Jun Cai, Na-Yu Chia, 2008

机译：GibbsModule跨物种从头鉴定顺式调控模块：在胚胎干细胞基因调控中的应用
7. The homotopy categorical crossed module of a CW-complex [O] . Carrasco P., Cegarra A.M., Garzón A.R. 2007

机译：CW复合体的同伦分类交叉模块

The homotopy categorical crossed module of a CW-complex

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