According to findagrave.com Memorial Number # 85029704 she was born in Glennascaul, Oranmore, Co. Galway on July 15th, 1886. According to her memorial her parents were James Ryder and Hannah Cooley and she married her husband John Brennan of Oranmore c. 1902. There is a Civil Record of a marriage between John Brennan, 27, of Glenacaul son of John Brennan, and Catherine Ryder of Carrowmanesh, daughter of Jame Ryder, for Feb. 19, 1903 in the RC parish of Oranmore. Catherine was only 16 years of age. There is a Civil Record for the marriage of James Ryder and Honor Cooly in Oranmore May 12, 1881, with daughter Catherine baptised July 20, 1886.
In the 1901 Census John Brennan was living with his uncle Michael Halpin in Glennascaul, Oranmore. Michael Halpin is an unmarried farmer. If this information is accurate it implies that John Brennan's mother's name was Halpin and this was later confirmed by his baptism record.
There is a baptism record for John Brennan, son of John Brennan and Margaret Halpin, June 14, 1875 in Oranmore RC Parish. His sponsors were (uncle) Michael Halpin and Catherine Kearney.
John Brennan and Margaret Halpin married Feb. 20, 1871 in Oranmore RC Parish. John Brennan's father was Patrick Brennan and Margaret Halpin's father was Laurence Halpin.
Another way of describing the family line; John Brennan of Oranmore's father was John and his paternal grandfather was Patrick. His mother was Margaret Halpin and his matenal grandfather was Laurence Halpin.
In the 1911 Census in Glennascaul, Oranmore, Kate Brennan is recorded as the Head of the Family and she was living with Lawrence age 7, John age 5, Bridget age 1 and James age 2 months. Uncle Michael Halpin (her husband's uncle) is still living and recorded as age 72. The whole family was born in Co. Galway.
In an interesting aside, the Constable/Enumerator was Michael Brennan.
By 1930, Catherine Ryder Brennan was living in Clementina Street San Francisco.