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- W3104607338 abstract "The concept of a pair of compatible actions was introduced in the case of groups by Brown and Loday and in the case of Lie algebras by Ellis. In this article we extend it to the context of semi-abelian categories (that satisfy the Smith-is-Huq condition). We give a new construction of the Peiffer product, which specialises to the definitions known for groups and Lie algebras. We use it to prove our main result, on the connection between pairs of compatible actions and pairs of crossed modules over a common base object. We also study the Peiffer product in its own right, in terms of its universal properties, and prove its equivalence with existing definitions in specific cases." @default.
- W3104607338 created "2020-11-23" @default.
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- W3104607338 date "2020-01-01" @default.
- W3104607338 modified "2023-10-14" @default.
- W3104607338 title "Compatible actions in semi-abelian categories" @default.
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- W3104607338 doi "https://doi.org/10.4310/hha.2020.v22.n2.a14" @default.
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