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arXiv · 1511.00824

Central reflections and nilpotency in exact Mal'tsev categories

Clemens Berger·Dominique Bourn
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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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Clemens Berger, Dominique Bourn. 2016-12-30. Central reflections and nilpotency in exact Mal'tsev categories. https://doi.org/10.1007/s40062-016-0165-8

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