No. “Objective red” is a definition. Depending on where it came from, it is but a social agreement, nothing more.
For example, the all hailed “wavelength of red” is a definition of red that shows up under certain precise conditions – lab conditions – highly controlled and artificial.
Cognition is reasoning powers and I am not conflating cognition with perception.
Rather, I am stating that what we consider objective is by tradition or authority or consensus – a mere group activity to make it easier to understand each other but has no bearing outside of its pragmatic usefulness in groups