Editing Restricted representation (section)

== Abstract algebraic setting ==
{{Main|Frobenius reciprocity}}
From the point of view of [[category theory]], restriction is an instance of a [[forgetful functor]]. This functor is [[exact functor|exact]], and its [[adjoint functor|left adjoint functor]] is called ''induction''. The relation between restriction and induction in various contexts is called the Frobenius reciprocity. Taken together, the operations of induction and restriction form a powerful set of tools for analyzing representations. This is especially true whenever the representations have the property of [[completely reducible|complete reducibility]], for example, in [[representation theory of finite groups]] over a [[field (algebra)|field]] of [[characteristic zero]].