Generalized Existential Completions and Applications in Lawvere Doctrines

Watch a 59-minute Topos Institute Colloquium talk exploring the concept of "generalized existential completion" in Lawvere doctrines and its practical applications. Dive into an algebraic characterization of existential-free formulas and discover how this framework helps identify various doctrinal examples, including subobjects doctrine, weak subobjects doctrine, realizability triposes, and supercoherent localic triposes. Learn about the construction's applications to dialectica interpretation, understanding how algebraic descriptions of quantifier-free formulas demonstrate logical principles in categorical settings. Based on collaborative research works by Maria Emilia Maietti, Davide Trotta, Matteo Spadetto, and Valeria de Paiva, gain insights into the relationship between logical systems and categorical frameworks through dialectica doctrines.