Group with operators: Difference between revisions

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is then an endomorphism of ''G''. From this, it results that a Ω-group can also be viewed as a group ''G'' with an [[indexed family]] <math>(u_{\omega})_{\omega \in \Omega}</math> of endomorphisms of ''G''.

<math>\Omega</math> is called the '''operator ___domain'''. The associate [[endomorphisms]]{{sfn|Bourbaki|1974|pp=30-3130–31}} are called the '''homotheties''' of ''G''.

Given two groups ''G'', ''H'' with same operator ___domain <math>\Omega</math>, a '''homomorphism''' of groups with operators is a group homomorphism ''f'':''G''<math>\to</math>''H'' satisfying

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== References ==

*{{cite book | ref=harv | last=Bourbaki | first=Nicolas | title=Elements of Mathematics : Algebra I Chapters 1-31–3 | publisher=Hermann | year=1974 | isbn=2-7056-5675-8}}

*{{cite book | ref=harv | last=Bourbaki | first=Nicolas | title=Elements of Mathematics : Algebra I Chapters 1-31–3 | publisher=Springer-Verlag | year=1998 | isbn=3-540-64243-9}}

*{{cite book | ref=harv | last=Mac Lane | first=Saunders | title=Categories for the Working Mathematician | publisher=Springer-Verlag | year=1998 | isbn=0-387-98403-8}}