  In this article we introduce conformal Riemannian morphisms. The idea of
conformal Riemannian morphism generalizes the notions of an isometric
immersion, a Riemannian submersion, an isometry, a Riemannian map and a
conformal Riemannian map. We show that every injective conformal Riemannian
morphism is an injective conformal immersion, and that on a connected manifold,
every surjective conformal Riemannian morphism is a surjective conformal
submersion, and every bijective conformal Riemannian morphism is a conformal
map.
