They were natives of Maigh Seóla, near Tuam, and originally of the Clann Cosgraigh, which was a branch of the Uí Briúin and kin to the Muintir Murchada.
The surname is nowadays rendered McHugh, or more rarely, McCoy.
Mac Áeda was elected archbishop of Tuam about March 1312, but not translated from Elphin until 19 December 1312, and did not receive possession of the temporalities until 1 April 1313.
He wrote what was described by O'Reilly as "a large volume of miscellaneous matter in Irish, containing, amongst other things, a catalogue of Irish kings from Niall Naoighiallach (Niall Noígíallach) to Roderick O'Conor (Ruaidrí Ua Conchobair).
Sir James Ware, in his account of Irish writers, says, it was extant in his time, and called the Book of Mac Aodha.