Central extensions in semi-abelian categories

Bourn, D;Gran, Marino
(2002) Journal of Pure and Applied Algebra — Vol. 175, n° 1-3, p. 31-44 (2002)

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Abstract
In the context of semi-abelian categories, we develop some new aspects of the categorical theory of central extensions by Janelidze and Kelly. If W is a semi-abelian category and X is any admissible subcategory we give several characterizations of trivial and central extensions. The notion of central extension becomes intrinsic when X is the subcategory of the abelian objects in W. We apply these results to the category of internal groupoids in a semi-abelian category. As a very special case, we get the known description of central extensions for crossed modules. (C) 2002 Elsevier Science B.V. All rights reserved.
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Bourn, D., & Gran, M. (2002). Central extensions in semi-abelian categories. Journal of Pure and Applied Algebra, 175(1-3), 31-44. https://doi.org/10.1016/S0022-4049(02)00127-5 (Original work published 2002)