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A frequent particular case occurs when f is a function from X to another set Y ; if x < sub > 1 </ sub > ~ x < sub > 2 </ sub > implies f ( x < sub > 1 </ sub >) = f ( x < sub > 2 </ sub >) then f is said to be a morphism for ~, a class invariant under ~, or simply invariant under ~.
This occurs, e. g. in the character theory of finite groups.
The latter case with the function f can be expressed by a commutative triangle.
See also invariant.
Some authors use " compatible with ~" or just " respects ~" instead of " invariant under ~".

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