In
mathematics, an
isomorphism (from the
Ancient Greek:
isos "equal", and
morphe "form" or "shape") is a
homomorphism (or more generally a
morphism) that admits an inverse. Two
mathematical objects are
isomorphic if an isomorphism exists between them. An
automorphism is an isomorphism whose source and target coincide. The interest of isomorphisms lies in the fact that two isomorphic objects cannot be distinguished by using only the properties used to define morphisms; thus isomorphic objects may be considered the same as long as one considers only these properties and their consequences.