What would you call a function $f$ with the property that $\forall y\in \text{img}(f)\left(\left|f^{-1}[\{y\}]\right|\in \mathbb{N}\right)$?
What about a function whose fibers all have the same cardinality?
Do either of these have a standard name? I'm trying to formalize a certain kind of map between objects, that should satisfy this and I don't want to make up notation if possible. It sorta reminds me of covering maps between topological spaces, though I can't think of the right word for this.