Crossed modules and Whitehead sequences

IF 0.5 4区数学 Journal of Homotopy and Related Structures Pub Date : 2016-10-13 DOI:10.1007/s40062-016-0159-6

Nelson Martins-Ferreira

引用次数: 3

Abstract

We introduce the notion of Whitehead sequence which is defined for a base category together with a system of abstract actions over it. In the classical case of groups and group actions the Whitehead sequences are precisely the crossed modules of groups. For a general setting we give sufficient conditions for the existence of a categorical equivalence between internal groupoids and Whitehead sequences.

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交叉模块和Whitehead序列

我们引入了Whitehead序列的概念，该概念是为一个基本范畴及其上的一组抽象动作所定义的。在群和群作用的经典情况下，Whitehead序列正是群的交叉模。在一般情况下，给出了内群与Whitehead序列之间存在范畴等价的充分条件。

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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Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

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