Help, Global studies at leat try to help?

Colonialism is just about colonies. England has colonies in Africa and India. France also had colonies in Africa. Couldn't the cultures mix for these to have happened. Doesn't the US have many Greek and Roman influences on our buildings. If it's ethnocentrism, then it's when these countries took over these other countries they ignored their culture and made them take their culture. (like when Rome overtook countries). I think it has to do more with cultural diffusion because of trading. When people traded, the got new ideas, materials, items, etc... Many cultures adapted these new things thus making a diffusion.