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:<math>\forall s \in S, \forall \omega \in \Omega : s^\omega \in S.</math>
== Category
In [[category theory]], a '''group with operators''' can be defined as an object of a [[functor category]] '''Grp'''<sup>'''M'''</sup> where '''M''' is a monoid (''i.e.'', a category with one object) and '''Grp''' denotes the [[category of groups]]. This definition is equivalent to the previous one.
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