Central reflections and nilpotency in exact Mal’tsev categories

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2016-12-23 DOI:10.1007/s40062-016-0165-8

Clemens Berger, Dominique Bourn

引用次数: 10

Abstract

We study nilpotency in the context of exact Mal’tsev categories taking central extensions as the primitive notion. This yields a nilpotency tower which is analysed from the perspective of Goodwillie’s functor calculus. We show in particular that the reflection into the subcategory of n-nilpotent objects is the universal endofunctor of degree n if and only if every n-nilpotent object is n-folded. In the special context of a semi-abelian category, an object is n-folded precisely when its Higgins commutator of length \(n+1\) vanishes.

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马尔采夫范畴的中心反射和幂零

我们在以中心扩展为原始概念的精确马尔采夫范畴的背景下研究幂零。这产生了一个零能塔，并从古德威利函子演算的角度对其进行了分析。我们特别证明了n个幂零对象的子范畴的反射是n次的泛函子，当且仅当每个n个幂零对象是n次折叠的。在半阿贝尔范畴的特殊情况下，当一个对象的长度为\(n+1\)的希金斯换易子消失时，它恰好是n折叠的。

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.