On the objects of the category of groups we define the mapping $G\mapsto \operatorname{Hol}(G)$, the holomorph $G\rtimes \operatorname{Aut}(G)$ of $G$. Can we extend this mapping to a functor on this category? (Via extension to morphisms)
Is $G\mapsto \operatorname{Hol}(G)$ the object component of any functor on the category of groups?
Ali Taghavi
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