Question: Mexican general, Gregorio Ruiz, fought against the ensuing empire of the younger brother of the Austrian emperor Francis Joseph I, the only what of the Second Mexican Empire?

Context paragraphs:
List of Vice Presidents of Mexico: The office of Vice President of Mexico was created by the Constitution of 1824, and was finally abolished by the current Constitution of 1917.  Many Mexican Vice Presidents acted as President during time between the end of the First Mexican Empire and the establishment of the Second Mexican Empire.

Gregorio Ruiz: Gregorio Ruiz was a Mexican general who participated in the Mexican Revolution.  He was born in Perote, Veracruz and he died in Mexico City in 1913.  He studied at the Heroico Colegio Militar, and by 1864 was a lieutenant of auxiliaries in the Mexican Army.  He fought against the French Intervention in Mexico and ensuing empire of Maximilian I of Mexico (1862–1867).  He participated in the pacification campaigns of Puebla and Oaxaca in 1876, and in Tepic and Sinaloa in 1877 and 1888.

Siege of Mexico City: The Siege of Mexico City was an 1867 military engagement in the French intervention in Mexico between Mexican Republican forces aided by the United States and Emperor Maximilian's troops aided by the French Empire and Austria-Hungary, encompassing in the siege of the city.  It was the last armed conflict of the Second Mexican Empire and the fall of the city resulted in the transition of the Empire into the Republic led by Benito Juárez.

Maximilian I of Mexico: Maximilian (Spanish: "Maximiliano"; born "Ferdinand Maximilian Joseph"; 6 July 1832 – 19 June 1867) was the only monarch of the Second Mexican Empire.  He was a younger brother of the Austrian emperor Francis Joseph I.  After a distinguished career in the Austrian Navy, he accepted an offer by Napoleon III of France to rule Mexico.  France (along with the United Kingdom and Spain, who both withdrew the following year after negotiating agreements with Mexico's democratic government) had invaded Mexico in the winter of 1861, as part of the War of the French Intervention.  Seeking to legitimize French rule in the Americas, Napoleon III invited Maximilian to establish a new Mexican monarchy for him.  With the support of the French army, and a group of conservative Mexican monarchists hostile to the liberal administration of new Mexican President Benito Juárez, Maximilian traveled to Mexico.  Once there, he declared himself Emperor of Mexico on 10 April 1864.

Guglielmo Oberdan: Guglielmo Oberdan, (born Wilhelm Oberdank) (February 1, 1858 - December 20, 1882) was an Italian irredentist.  He was executed after a failed attempt to assassinate Austrian Emperor Francis Joseph, becoming a martyr of the Italian unification movement.

Second Mexican Empire: The Mexican Empire (Spanish: "Imperio Mexicano" ) or Second Mexican Empire (Spanish: "Segundo Imperio Mexicano" ) was the name of Mexico under a limited hereditary monarchy declared by the Assembly of Notables on July 10, 1863, during the Second French intervention in Mexico.  It was created with the support of Napoleon III of France, who attempted to establish a monarchist ally in the Americas.  A referendum confirmed Austrian Archduke Ferdinand Maximilian, of the House of Habsburg-Lorraine, as Emperor Maximilian I of Mexico.

Battle of Miahuatlán: The Battle of Miahuatlán took place on 3 October 1866 in the vicinity of the current municipality of Miahuatlán de Porfirio Díaz in the state of Oaxaca, Mexico.  It was fought between elements of the Mexican republican army under General Porfirio Díaz and troops of the Second Mexican Empire during the French intervention in Mexico.

Guadalupe Victoria: Guadalupe Victoria (] ; 29 September 1786 – 21 March 1843), born José Miguel Ramón Adaucto Fernández y Félix, was a Mexican general and political leader who fought for independence against the Spanish Empire in the Mexican War of Independence.  He was a deputy in the Mexican Chamber of Deputies for Durango and a member of the Supreme Executive Power following the downfall of the First Mexican Empire.  After the adoption of the Constitution of 1824, Victoria was elected as the first President of the United Mexican States.

José Mariano Salas: José Mariano de Salas (11 May 1797 – 24 December 1867) was a Mexican general and politician who served twice as interim president of Mexico (1846 and 1859).  He was also a member of the executive triumvirate of the Second Mexican Empire that invited Maximilian of Habsburg to take the throne.

Battle of Cerro del Borrego: The Battle of Cerro del Borrego took place on 13 June 1862 in the vicinity of the current municipality of Orizaba in the state of Veracruz, Mexico.  It was fought between the Mexican republican army under General Jesús Gonzalez Ortega and troops of the Second Mexican Empire during the French intervention in Mexico.

Supporting paragraphs: Gregorio Ruiz Maximilian I of Mexico
Answer: monarch