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Normal functors and strong protomodularity

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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,
Mal’cev 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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