The Last Samurai

Former US Army Captain Nathan Algren, a bitter alcoholic traumatized by the atrocities he committed during the American Indian Wars, is approached by his former commanding officer Colonel Bagley to train the newly formed Imperial Japanese Army for Japanese businessman Omura, who intends to use the army to suppress a samurai-headed rebellion against Japan's new Emperor. Despite his hatred of Bagley for his role in the Indian Wars, an impoverished Algren takes the job for the money, and is accompanied to Japan by his old friend Sergeant Zebulon Gant and Simon Graham, a British translator knowledgeable about the Samurai.
Algren finds the Imperial soldiers are poorly-trained; rather than finding an eager army, he finds conscripted peasants that have no knowledge of firearms. During training, Algren is informed that the samurai are attacking one of Omura's railroads; Omura sends the army there, despite his protests. The battle is a disaster; the conscripts panic, and Gant is killed in the battle. Algren kills several samurai before he is surrounded; expecting to die, he is surprised when samurai leader Katsumoto decides to spare him. Algren is taken to the Katsumoto's village to live among his family. While he is poorly treated by the samurai at first, he eventually gains their respect. Algren overcomes his alcoholism and guilt over his past sins, learns the Japanese language and culture, and develops sympathy for the Samurai, who are angry that the spread of modern technology has eroded traditional feudalism and the status and power of the Samurai. Algren becomes close with Taka, Katsumoto's sister and the widow of a Samurai Algren killed.
One night, as the village is watching a kabuki play, a group of ninjas, sent by Omura, infiltrate the village and attempt to assassinate Katsumoto. However, Algren notices them and warns Katsumoto in time, saving his life. In the ensuing battle, Algren helps defend Katsumoto's family, earning his respect. Katsumoto requests a meeting with Emperor Meiji and is given safe passage to Tokyo, bringing Algren along with the intent to release him. Upon arriving in Tokyo, Algren finds the Imperial Army is now a well-trained and equipped fighting force, while Katsumoto, to his dismay, discovers that the Emperor is essentially a puppet of Omura. At a government meeting, Omura orders Katsumoto's arrest for carrying a sword in public and asks him to commit seppuku to redeem his honor. When Algren refuses Omura's offer to lead the new army to crush the rebels, Omura orders him killed as well. Omura sends assassins to kill Algren, but Algren kills his assailants. Algren and Katsumoto's samurai arrive to free Katsumoto from the Imperial Army. They manage to rescue him; however, in the process, Katsumoto's son, Nobutada is wounded, and he sacrifices himself to allow the others to escape.
As the Imperial Army marches to crush the rebellion, a grieving Katsumoto contemplates seppuku, but Algren convinces him to fight until the end, and joins the samurai in battle. Citing the Battle of Thermopylae, the Samurai use the Imperial Army's overconfidence to lure their soldiers into a trap and deprives them of artillery support. The ensuing mÃªlÃ©e battle inflicts massive casualties on both sides and forces the Imperial soldiers to retreat. Knowing that Imperial reinforcements are coming and defeat is inevitable, Katsumoto orders a suicidal charge on horseback. During the charge, they break through Bagley's line, and Algren kills Bagley in battle. They rush through his line, and are quickly mowed down by gatling guns. The Imperial captain, previously trained by Algren, is moved by the sight of dying samurai and disobeys Omura's orders, ordering all of the guns to stop. A mortally-wounded Katsumoto commits seppuku with Algren's help. The soldiers present in the scene kneel down in respect for the fallen Samurai.
Days later, as trade negotiations conclude, Algren, though injured, arrives and interrupts the proceedings. He presents the Emperor with Katsumoto's sword and asks him to remember the traditions for which Katsumoto died. The Emperor realizes that while Japan should continue its foreign interaction with other countries, it also should remember its own culture and history. He rejects trade offer; when Omura protests his decision, the Emperor decides to seize the Omura family assets and distribute them to the poor. Algren returns to the village to Taka; while various rumors about Algren start to circulate, Graham concludes that Algren has finally found peace in his life.

Question: Who does Algren kill?
Answer: Bagley