A frequent particular case occurs when "f" is a function from "X" to another set "Y"; if "x"1 ~ "x"2 implies "f"("x"1) = "f"("x"2) 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 ~".