A note on split extension classifiers of perfect objects

2022/08/01 by Gray, James R. A.
#Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.01133

Abstract

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

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