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- W3202019063 abstract "We introduce the notions of proto-complete, complete, complete⁎ and strong-complete objects in pointed categories. We show under mild conditions on a pointed exact protomodular category that every proto-complete (respectively complete) object is the product of an abelian proto-complete (respectively complete) object and a strong-complete object. This together with the observation that the trivial group is the only abelian complete group recovers a theorem of Baer classifying complete groups. In addition we generalize several theorems about groups (subgroups) with trivial center (respectively, centralizer), and provide a categorical explanation behind why the derivation algebra of a perfect Lie algebra with trivial center and the automorphism group of a non-abelian (characteristically) simple group are strong-complete." @default.
- W3202019063 created "2021-10-11" @default.
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- W3202019063 date "2022-04-01" @default.
- W3202019063 modified "2023-09-25" @default.
- W3202019063 title "Complete objects in categories" @default.
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- W3202019063 doi "https://doi.org/10.1016/j.jpaa.2021.106857" @default.
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