Final answer:
The rebellion of American settlers against the Mexican government of California was called the Bear Flag Rebellion, which led to a brief establishment of the California Republic before ultimately being absorbed into the United States.
Step-by-step explanation:
The rebellion of American settlers against the Mexican government of California was called the Bear Flag Rebellion.
In June of 1846, during the period leading up to the Mexican-American War, a group of American settlers in California, along with some supportive Californios, rebelled against the Mexican government and captured the garrison at Sonoma, California. This event was part of the U.S. strategy for a three-pronged attack on Mexico, aiming for the occupation of Mexican territories by different military contingents. Upon seizing the garrison, they proclaimed a new government, calling it the California Republic, though this entity would only last less than a month. The peaceful rebellion highlighted the instability of the Mexican government's control over California, with leadership having changed hands numerous times in the previous 25 years.
The California Republic fell when John Frémont and his corps of engineers arrived, marking the region's annexation to the United States soon after. All these events serve as a part of the larger backdrop, including the Mexican-American War, the eventual discovery of gold in California, and the rapid American settlement that ensues at the expense of Native Americans, Mexicans, and Mexican-Americans.