We introduced in a previous article a notion of Mal'tsevness relative to a specific class $\Sigma$ of split epimorphisms. We investigate here the induced relative notion of natural Mal'tsevness, with a special attention to the example of quandles.
Keywords: Fibration of points, Mal'tsev, protomodular, naturally Mal'tsev and additive categories; internal groupoids.}
2010 MSC: 18C99, 18A10, 08B05, 57M27
Theory and Applications of Categories, Vol. 31, 2016, No. 15, pp 418-443.