There are 2 mentions of the firm in the UK's National Archives as Percival, Yates and Co, which appear to be letters in respect of the EXHIBITION OF THE WORKS OF INDUSTRY OF ALL NATIONS, LONDON, 1 MAY - 15 OCTOBER 1851 (i.e. The Great Exhibition of 1851).
Title: To Thos. Worthington. From Messrs. Percival, Yates and Co., British and Foreign Flint Glass Works, Manchester, withdrawing from Exhibition as space allotted is too small.
Reference: M6/3/11/239-240
Date: 27 Feb 1851
Held by: Manchester Archives and Local Studies, not available at The National Archives
Language: English
and
Title: From C. Pasley, Lt. R.E., Superintendent of Class 24, for M.D. Wyatt, to same, allowing Messrs. Molineaux, Webb and Co. the space formerly allocated to Percival, Yates and Co.
Reference: M6/3/8/350
Date: 28 Feb 1851
Held by: Manchester Archives and Local Studies, not available at The National Archives
Language: English
I suspect Yeates is a more common surname in Ireland so it's an understandable mistake in the Dublin exhibition catalogue.