They didn't. The crusades ended before America was colonized.
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The battle was a result of colonialism. Although the era of colonialism was ending around the world, it was not ending in Algeria which revolted against French rule.
Colonialism devastated the Libyan economy and held it back for many years.
Mexico had a sense of colonialism over Texas before they gained independence.
The most noticeable effect that is likely a result of colonization is Cuba's current government. Cuba's colonization opened the door to later US interference. In an effort to escape both America's hold and its own economic struggles, Cuba turned to the Communists in Russia for help.
European nations were able to generate new trade routes overseas