I recently starded studying the book "Orbifolds and Stringy Topology" by Adem, Leida and Ruan and I'm trying to see if there is a relation between the singularites of two orbifolds when there is a smooth map from one to another. More precisely:
Let $X$ and $Y$ be smooth orbifolds and $f:X \rightarrow Y$ a smooth map. What would be a sufficient condition under which the image of a singular point is also a singular point?