Question: Which Roman Emperor was grandfather to the children of Mark Antony?

Passages:
The Caesareum of Alexandria is an ancient temple in Alexandria, Egypt.  It was conceived by Cleopatra VII of the Ptolemaic kingdom, the last pharaoh of Ancient Egypt, to honour her dead lover Marc Antony.  The edifice was finished by the Roman Emperor Augustus, after he defeated Mark Antony and Cleopatra.  He destroyed all traces of Antony in Alexandria, and apparently dedicated the temple to his own cult. <P3-S0> Claudia Marcella was the name of the two daughters of Octavia Minor, the sister of Roman emperor Augustus, by her first husband, the consul Gaius Claudius Marcellus. <P3-S1>  According to the Roman Historian Suetonius, they were known as The Marcellae sisters, and they are also known as the two Marcellae. <P3-S2>  The sisters were born in Rome. <P3-S3>  Between 40 BC-36 BC, they lived with their mother and their stepfather Triumvir Mark Antony in Athens, Greece. <P3-S4>  After 36 BC they accompanied their mother when she returned to Rome with their siblings. <P3-S5>  They were raised and educated by their mother, their maternal uncle, Roman emperor Augustus, and their maternal aunt-in-marriage Roman Empress Livia Drusilla. <P3-S6>  These two daughters of Octavia Minor and Gaius Claudius Marcellus with their siblings, provide a critical link between the past of the Roman Republic and the new Roman Empire. <P3-S7>  The marriages of the sisters and the children born to their unions assured republican family lines into the next generation. Caligula ( ), properly Gaius Julius Caesar Augustus Germanicus (31 August AD 12 – 24 January AD 41) was Roman emperor from AD 37–41.  Born Gaius Julius Caesar Germanicus (not to be confused with Julius Caesar), Caligula was a member of the house of rulers conventionally known as the Julio-Claudian dynasty.  Caligula's biological father was Germanicus, and he was the great-nephew and adopted son of Emperor Tiberius.  The young Gaius earned the nickname "Caligula" (meaning "little soldier's boot", the diminutive form of "caliga", hob-nailed military boot) from his father's soldiers while accompanying him during his campaigns in Germania. Augustus (Latin: "Imperātor Caesar Dīvī Fīlius Augustus" ; 23 September 63 BC – 19 August 14 AD) was the founder of the Roman Principate and considered the first Roman emperor, controlling the Roman Empire from 27 BC until his death in AD 14.  He was born Gaius Octavius into an old and wealthy equestrian branch of the plebeian "gens" Octavia.  His maternal great-uncle Julius Caesar was assassinated in 44 BC, and Octavius was named in Caesar's will as his adopted son and heir, then known as Octavianus (Anglicized as Octavian).  He, Mark Antony, and Marcus Lepidus formed the Second Triumvirate to defeat the assassins of Caesar.  Following their victory at the Battle of Philippi, the Triumvirate divided the Roman Republic among themselves and ruled as military dictators.  The Triumvirate was eventually torn apart by the competing ambitions of its members.  Lepidus was driven into exile and stripped of his position, and Antony committed suicide following his defeat at the Battle of Actium by Octavian in 31 BC. Annia Aurelia Fadilla, most commonly known as Fadilla (159-died after 211) was an influential Roman Princess and was one of the daughters born to Roman Emperor Marcus Aurelius and Roman Empress Faustina the Younger.  She was a sister to Roman Empress Lucilla and Roman Emperor Commodus.  Fadilla was named in honor of her late maternal aunt Aurelia Fadilla.  The cognomen Fadilla, was the cognomen of the mother and a half-sister of the previous Roman Emperor Antoninus Pius.  Her maternal grandparents were Roman Emperor Antoninus Pius and Roman Empress Faustina the Elder and her paternal grandparents were Domitia Lucilla and praetor Marcus Annius Verus. The Final War of the Roman Republic, also known as Antony's Civil War or The War between Antony and Octavian, was the last of the Roman civil wars of the republic, fought between Mark Antony (assisted by Cleopatra) and Octavian.  After the Roman Senate declared war on the Egyptian queen Cleopatra, Antony, her lover and ally, betrayed the Roman government and joined the war on Cleopatra’s side.  After the decisive victory for Octavian at the Battle of Actium, Cleopatra and Antony withdrew to Alexandria, where Octavian besieged the city until both Antony and Cleopatra committed suicide. Marcia Servilia Sorana or commonly known as Servilia (40s-66) was the daughter of Roman Senator Quintus Marcius Barea Soranus and her mother may have been from the gens Servilia.  Servilia's paternal uncle was the Roman Senator Quintus Marcius Barea Sura, who was a friend to the future Roman Emperor Vespasian.  Her paternal cousins were Marcia (mother of Ulpia Marciana and of future Roman Emperor Trajan) and Marcia Furnilla (the second wife of the future Roman Emperor Titus).  Her paternal grandfather Quintus Marcius Barea Soranus was Suffect Consul in 34 and twice Proconsul of Africa. Antonia Minor ("PIR" A 885), also known as Julia Antonia Minor, Antonia the Younger or simply Antonia (31 January 36 BC - September/October AD 37) was the younger of two daughters of Mark Antony and Octavia Minor.  She was a niece of the Emperor Augustus, sister-in-law of the Emperor Tiberius, paternal grandmother of the Emperor Caligula and Empress Agrippina the Younger, mother of the Emperor Claudius, and both maternal great-grandmother and paternal great-aunt of the Emperor Nero.  She was additionally the maternal great-aunt of the Empress Valeria Messalina and Faustus Cornelius Sulla Felix, the paternal grandmother of Claudia Antonia, Claudia Octavia, and Britannicus and the maternal grandmother of Julia Livia and Tiberius Gemellus. <P0-S0> Marcus Vipsanius Agrippa ( ; 64/62 BC – 12 BC) was a Roman consul, statesman, general and architect. <P0-S1>  He was a close friend, son-in-law, and lieutenant to Octavian and was responsible for the construction of some of the most notable buildings in the history of Rome and for important military victories, most notably at the Battle of Actium in 31 BC against the forces of Mark Antony and Cleopatra. <P0-S2>  As a result of these victories Octavian became the first Roman Emperor, adopting the name of Augustus. <P0-S3>  Agrippa assisted Augustus in making Rome a city of marble and renovating aqueducts to give all Romans, from every social class, access to the highest quality public services. <P0-S4>  He was responsible for the creation of many baths, porticoes and gardens, as well as the original Pantheon. <P0-S5>  Agrippa was also father-in-law to the second Emperor Tiberius, maternal grandfather to Caligula, and maternal great-grandfather to the Emperor Nero. Domitia ("PIR²" D 171), more commonly referred to as Domitia the Elder -- in fact no ancient source ever calls her Lepida - (ca. 8 BC-June 59) was the oldest child of Antonia Major and Lucius Domitius Ahenobarbus (consul 16 BC), and the oldest granddaughter to Triumvir Mark Antony by Octavia Minor, a great-niece of the Roman Emperor Augustus, second cousin and sister-in-law to the Emperor Caligula, first cousin to the Emperor Claudius, maternal aunt to the Empress Valeria Messalina, and paternal aunt to Emperor Nero.  She had two younger siblings: Domitia Lepida and Cn.  Domitius Ahenobarbus (cos.  AD 32).  The date of her birth is not recorded and can be only estimated as no later than 7 BC, but possibly as much as 10 years earlier, if one would allow a long delay between her birth and those of her two siblings.

Supporting sentences:
 She was a niece of the Emperor Augustus, sister-in-law of the Emperor Tiberius, paternal grandmother of the Emperor Caligula and Empress Agrippina the Younger, mother of the Emperor Claudius, and both maternal great-grandmother and paternal great-aunt of the Emperor Nero. Caligula ( ), properly Gaius Julius Caesar Augustus Germanicus (31 August AD 12 – 24 January AD 41) was Roman emperor from AD 37–41.