Abstract
We propose relative (to a distinguished class E of epimorphisms) versions of the so-called old and new style axioms for semi-abelian categories, and prove the equivalence of these two sets of axioms. The same results were obtained before under much stronger completeness/cocompleteness assumptions. One of obvious purposes of such a generalization is to include the trivial case of E being the class of all isomorphisms when the ground category is an arbitrary pointed category.
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Dedicated to the memory of Gregory Maxwell Kelly.
Partially supported by the International Student Scholarship of the University of Cape Town, and Georgian National Science Foundation (GNSF/ST06/3-004).
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Janelidze, T. Incomplete Relative Semi-Abelian Categories. Appl Categor Struct 19, 257–270 (2011). https://doi.org/10.1007/s10485-009-9193-4
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DOI: https://doi.org/10.1007/s10485-009-9193-4
Keywords
- Incomplete relative semi-abelian category
- Relative semi-abelian category
- Semi-abelian category
- Relative homological category
- Regular epimorphism
- Normal epimorphism