On preview, I see this has already been answered, but the Roman numerals apply in any key, not just C.
I is always the root of the key for major keys.
So, in E-flat, you’d have E-flat, Fm, Gm, A-flat, B-flat, Cm, D-dim, E-flat
The numbers are based on the triads created based on walking up the (in this case, major) scale of the key: E-flat, F, G, A-flat, B-flat, C, D, E-flat.
I: E-flat, G, B-flat
ii: F, A-flat, C
iii: G, B-flat, D
IV: A-flat, C, E-flat
V: B-flat, D, F
vi: C, E-flat, G
vii-dim: D, F, A-flat
I: E-flat, G, B-flat
The chord structures are a little different for minor keys.