Unifying mathematics through topos theory

The paper "The unification of Mathematics via Topos Theory", written in 2010 and recently published in the book "Logic in Question. Studies in Universal Logic", introduced a set of principles and methodologies for unifying distinct mathematical theories with each other, resulting from a new view of Grothendieck toposes as “bridge” objects for transferring information, ideas, and results between different mathematical contexts. We shall make a survey of the theoretical principles underlying the use of toposes as unifying 'bridges', as well as of the further developments and notable applications of this theory obtained throughout the past years.