Using the framework of categorical logic, this paper analyzes and streamlines Gabbay's semantical proof of the Craig interpolation theorem for intuitionistic predicate logic. In the process, an apparently new and interesting fact about the relation of coherent and intuitionistic logic is found.
"On Gabbay's Proof of the Craig Interpolation Theorem for Intuitionistic Predicate Logic." Notre Dame J. Formal Logic 36 (3) 364 - 381, Summer 1995. https://doi.org/10.1305/ndjfl/1040149353