The buildings and people that Bloom sees on "the dead side of the street" in Hades are "Under the patronage of the late Father Mathew" because a statue to that man stands in the middle of Upper Sackville (now O'Connell) Street, extending its hands in the blessing that comes from abstaining from alcohol. Gerty MacDowell wishes her father had benefited from the good father's teaching.
Later in the day, Blazes Boylan retraces part of the path followed by the funeral cortège, traveling north from the quays along Sackville Street in a jaunting car toward the Blooms' house. Sirens mentions his passing many of the same urban landmarks passed by Bloom in the morning: Sir John Gray's statue, Nelson's pillar, Elvery's, Father Mathew, the Rotunda.
Gareth Collins summarizes the friar's social significance:
Mathew (1790-1856) was a Cork-based Capuchin friar, born in County Tipperary, who led a great temperance movement from 1839 to1856. His anti-drink campaign is considered to have been a great social revolution that saw the establishment of Temperance Societies in every parish in the country. At its peak between 1838-1845, it was estimated that there were 3-4 million abstaining from drink in Ireland. This high number was aided by the fact that Fr Mathew appealed to every class and rank in society. In 1843, Fr Mathew went to England and Scotland where he had further success, and later spent over two years in the US where he gave the pledge in over 300 towns. He's also famous for his work during the cholera epidemic of 1832 and The Great Famine. The statue was erected in 1891 by sculptor Mary Redmond."
Echoes of the temperance movement sound throughout Ulysses—not surprising when one considers that more than half the population of Ireland took Father Mathew's "pledge" to abstain from drink in the 1840s, and people were still taking it in 1904. When Gerty MacDowell thinks of her father's ruinous alcoholism, she wishes that he might have taken the pledge: "Had her father only avoided the clutches of the demon drink, by taking the pledge or those powders the drink habit cured in Pearson's Weekly, she might now be rolling in her carriage, second to none." People who took the pledge were expected to adhere to it for life, by a commitment of will as absolute as marriage vows.
The pledge movement began in Cork with the establishment of the Cork Total Abstinence Society in 1838. Another statue to Father Mathew's memory stands in Cork, on St. Patrick's Street. It was erected in 1864.