Normal functors and strong protomodularity

Dominique Bourn

The notion of normal subobject having an intrinsic meaning in any protomodular category, we introduce the notion of normal functor, namely left exact conservative functor which reflects normal subobjects. The point is that for the category {\bf Gp} of groups the change of base functors, with respect to the fibration of pointed objects, are not only conservative (this is the definition of a protomodular category), but also normal. This leads to the notion of strongly protomodular category. Some of their properties are given, the main one being that this notion is inherited by the slice categories.

Keywords: abstract normal subobject, preservation and reflection of normal subobject, Malícev and protomodular categories.

2000 MSC: 18D05,08B05,18G30,20L17.

Theory and Applications of Categories, Vol. 7, 2000, No. 9, pp 205-218.

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