We define relative regular Mal'tsev categories and give an overview of conditions which are equivalent to the relative Mal'tsev axiom. These include conditions on relations as well as conditions on simplicial objects. We also give various examples and counterexamples.
Keywords: higher extension; simplicial resolution; Mal'tsev condition; relative homological algebra; arithmetical category
2010 MSC: 18A20, 18E10, 18G25, 18G30, 20J
Theory and Applications of Categories, Vol. 28, 2013, No. 29, pp 1002-1021.
Published 2013-10-14.
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