  Given two two-dimensional conformal field theories, a domain wall -- or
defect line -- between them is called invertible if there is another defect
with which it fuses to the identity defect. A defect is called topological if
it is transparent to the stress tensor. A conformal isomorphism between the two
CFTs is a linear isomorphism between their state spaces which preserves the
stress tensor and is compatible with the operator product expansion. We show
that for rational CFTs there is a one-to-one correspondence between invertible
topological defects and conformal isomorphisms if both preserve the rational
symmetry. This correspondence is compatible with composition.
