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Composites of Central Extensions Form a Relative Semi-Abelian Category

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Abstract

We consider trivial and central extensions, in the sense of G. Janelidze and G. M. Kelly, which are defined with respect to an adjunction between a Barr-exact category C and a Birkhoff subcategory X of C. Assuming in addition that C is a pointed Mal’tsev category with cokernels, and that X is protomodular, we prove that: (a) the class of all trivial extensions and the class of all finite composites of central extensions form relative homological category structures on C; (b) if C has finite coproducts, then the class of all finite composites of central extensions forms a relative semi-abelian category structure on C.

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Authors and Affiliations

  1. Department of Mathematical Sciences, College of Science, Engineering and Technology, University of South Africa, Cnr Christiaan de Wet & Pioneer Avenue, Florida, PO Box 392, 0003, Pretoria, South Africa

    Tamar Janelidze-Gray

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  1. Tamar Janelidze-Gray
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Correspondence to Tamar Janelidze-Gray.

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Dedicated to my father George Janelidze on the occasion of his 60th birthday

Supported by the University of South Africa Postdoctoral Fellowship

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Janelidze-Gray, T. Composites of Central Extensions Form a Relative Semi-Abelian Category. Appl Categor Struct 22, 857–872 (2014). https://doi.org/10.1007/s10485-013-9354-3

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