I know that in Ring Category we have:
-Arrows: Ring homomorphisms.
I do not know which are the objects and arrows in Graded Ring Category. In general, which is the definition of Graded Ring Category?
P.S. I need it in order to see why it makes a difference to take inverse limit in this two categories. (I am working in symmetric functions vs symmetric polynomials. Do not see the difference between this two concepts.)