Groups up to congruence relation and from categorical groups to c-crossed modules

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2020-11-21 DOI:10.1007/s40062-020-00270-4

Tamar Datuashvili, Osman Mucuk, Tunçar Şahan

引用次数: 0

Abstract

We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is constructed. We prove that each categorical group gives rise to a c-group and to a c-crossed module, which is a connected, special and strict c-crossed module in the sense defined by us. The results obtained here will be applied in the proof of an equivalence of the categories of categorical groups and connected, special and strict c-crossed modules.

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到同余关系的群和从范畴群到c交叉模的群

引入c群的概念，c群是一个达到同余关系的群，并考虑其相应的范畴。在此范畴中定义了扩展、动作和交叉模块(c交叉模块)，并构造了半直接积。证明了每一个范畴群都产生一个c群和一个c交叉模，这个c交叉模是我们定义的意义上的连通的、特殊的、严格的c交叉模。所得结果将用于证明纯群和连通、特殊、严格c交叉模的一类等价性。

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

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.