Precrossed modules and Galois theory
(2006) Journal of Algebra — Vol. 297, n° 1, p. 292-309 (2006)
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- Abstract
- The adjunction between crossed modules and precrossed modules over a fixed group can be seen as a special case of a more general adjunction between internal groupoids and internal reflexive graphs in a Mal'tsev variety. By using the categorical Galois theory, we characterize the central extensions with respect to this latter adjunction in terms of the universal algebraic commutator. In particular, we get a description of the central extensions of precrossed modules and of precrossed rings. This characterization provides a natural way to define a categorical notion of Peiffer commutator. (c) 2005 Elsevier Inc. All rights reserved.
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Everaert, T., & Gran, M. (2006). Precrossed modules and Galois theory. Journal of Algebra, 297(1), 292-309. https://doi.org/10.1016/j.jalgebra.2005.06.034 (Original work published 2006)