In Physics, there is the index of refraction $n$. Sometimes, it will be just a scalar, sometimes it will be a function of the wave number $k$. I often see $n = n(k)$ to denote that $n$ is actually a function of $k$. Since in Physics the function arguments are often omitted, this kind of works.
But I would think (maybe more from a programming perspective) that $n$ is a function then and $n(k)$ a scalar, the value of $n$ at $k$.
Would it be only correct to write $n \colon k \mapsto n(k)$ in such situtations?