In mathematics, representation is a very general relationship that expresses similarities between objects. Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y_i conform in some consistent way to those existing among the corresponding represented objects x_i. Somewhat more formally, for a set Π of properties and relations, a Π-representation of some structure X is a structure Y that is the image of X under a homomorphism that preserves Π. The label representation is sometimes also applied to the homomorphism itself.