His first work of importance was a new edition of Ferdinando Ughelli's Italia Sacra published in ten volumes from 1717 to 1722.

Besides correcting many errors, Coleti continued Ughelli's history to the beginning of the eighteenth century.

Up to this time there had been two standard histories of the councils, Sacrorum conciliorum nova et amplissima collectio by Philippe Labbe and Gabriel Cossart (1671–72), its supplement compiled by Étienne Baluze (of which only the first volume was published), and the collection of Jean Hardouin (1715).

Other works of Coleti's were Series episcoporum Cremonensium aucta (1749), and Monumenta ecclesiæ Venetæ S. Moisis (1758).

Coleti also annotated a manuscript of Scipione Maffei, now preserved in the Biblioteca Vallicelliana at Rome.