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arXiv · 2208.01133

A note on split extension classifiers of perfect objects

James R. A. Gray
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Abstract

We show that for a pointed protomodular category $\mathbb{C}$ satisfying a certain condition on those Huq commutators which exist, if $X$ is a perfect object in $\mathbb{C}$ such that the split extension classifier $[X]$ exists, then the centralizer of the \emph{conjugation} morphism $c_X : X\to [X]$ is trivial and hence $[X]$ has trivial center.

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James R. A. Gray. 2022-08-01. A note on split extension classifiers of perfect objects. https://arxiv.org/abs/2208.01133

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