Question for the Colorado CCW law gurus: is licensed CCW on a university campus forbidden by state or federal law?

My reading of federal law has shown me that it is prohibited unless the state has issued you a permit to carry. The state can still outlaw carry essentially anywhere they want, and that you must abide by.

My reading of state law is "A permit issued pursuant to this part 2 does not authorize a person to carry a concealed handgun onto the real property, or into any improvements erected thereon, of a public elementary, middle, junior high, or high school; except that..."

If I'm not mistaken a CCW permit holder may legally carry on the grounds of a public or private university in the state of Colorado. No?

Thanks in advance!