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YCor
YCor
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Is $G\mapsto Hol\operatorname{Hol}(G)$ the object component of any functor on the category of groups?

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

Is $G\mapsto Hol(G)$ the object component of any functor on the category of groups?

On the objects of the category of groups we define the mapping $G\mapsto Hol(G)$, the holomorph $G\rtimes Aut(G)$ of $G$. Can we extend this mapping to a functor on this category?(Via extention to morphisms)

Is $G\mapsto \operatorname{Hol}(G)$ the object component of any functor on the category of groups?

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)

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Ali Taghavi
Ali Taghavi
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Can Is $G\mapsto Hol(G)$ be counted as athe object component of any functor on the category of groups?

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Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

Can $G\mapsto Hol(G)$ be counted as a functor on the category of groups?

On the objects of the category of groups we define the mapping $G\mapsto Hol(G)$, the holomorph $G\rtimes Aut(G)$ of $G$. Can we extend this mapping to a functor on this category?(Via extention to morphisms)