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
yi conform in some consistent way to those existing among the corresponding represented objects
xi. 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.