General term for map/fmap The general term for folds is a catamorphism. The general term for unfold is an Anamorphism. Is there an equivalent term for map?  I know that a map is a type of fold however restriction is significant.  Also it would be useful to have an alternative term to use when the word “map” is ambiguous.
In addition to being in agreement with Derek (that the ana/cata terminology doesn't bring much to the table) I'll note that the "category theoretic" terminology for the general map function of type
$$\mathrm{map}:\forall \alpha\beta. (\alpha \rightarrow\beta)\rightarrow(F\ \alpha\rightarrow F\beta) $$
for a functor $F$ is simply "the functorial action of $F$", and is often written as $F$! For example, on lists, map f l would be written $\mathrm{List}(f)(l)$.

For some reason, computer scientists seem to prefer to have a seperate name for the type constructor and the action on morphisms, but mathematicians do not really consider non-functorial constructors anyways.