@RyderRude Because a group is a groupoid with one object, commonly called *.

The functor sends * to X in Set, which is the set that it is acting on

The group elements, which are automorphisms of *, naturally become automorphisms of the set X.

Hope this clears things up for you

What do we call the solution to the Helmholtz equation?

Can we have in real life, only linear polarized light? Wouldn't that be impossible, as a linearly polarized light, implies one frequency i.e a plane wave, and plane waves are not physical ?

@imbAF It depends on the context

what do you mean?

You have vibrating membrane interpretations, Laplace equations (which give electrostatic field), quantum mechanical free particle interpretations, etc

plus, depending on the experiment it may not matter if the light isn't "perfectly" linearly polarized

it just has to be close enough to linearly-polarized for it to interact with other objects in interesting ways