Construct functors as follows: (a) A covariant functor G S that assigns to each group the

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Construct functors as follows:

(a) A covariant functor G  → S that assigns to each group the set of all its subgroups.

(b) A covariant functor R → R that assigns to each ring N the polynomial ring N[x].

(c) A functor, covariant in both variablesSuch that

(d) A covariant functor G → G that assigns to each group G its commutator subgroup G' 

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