# A 1-1 function is called injective. What is an n-1 function called?

A 1-1 function is called injective. What is an n-1 function called ?

I'm thinking about homomorphisms. So perhaps homojective ?

Onto is surjective. 1-1 and onto is bijective.

What about n-1 and onto ? Projective ? Polyjective ?

I think n-m and onto should be hyperjective as in hypergroups.

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n-jective? :) ... –  Blue Sep 3 '10 at 7:17
These aren't called anything in particular, but I've seen algebraic geometers denote that a function is $n$ to $1$ by writing $n:1$ above an arrow between sets. You have to keep in mind that these functions usually arise either as finite covering maps or polynomials (or both at the same time), so it's usually clear when one actually has to use that a given function has that property. –  Gunnar Magnusson Nov 24 '10 at 21:59
A slightly related concept from complex function theory and the theory of automorphic functions is valence. A holomorphic function on an open domain of the complex plane is said to be univalent if it is 1-to-1, and $p$-valent if it is at most $p$-to-1. See also eom.springer.de/m/m065560.htm –  Willie Wong Nov 25 '10 at 0:09