An Introduction to the Theory of Lawvere's Doctrines and its Recent Advances

Explore a nearly two-hour seminar presentation from the Orange County Inland Empire (OCIE) Series in History and Philosophy of Mathematics, delivered at Chapman University by Jacopo Emmenegger. Delve into the fundamental concepts of Lawvere's doctrines, originally developed as algebraic tools for working with logical theories and their extensions. Learn how doctrines provide a framework for addressing complex questions about theory construction and logical structure addition. Examine the algebraic character of doctrine theory and its applications in logic and type theory, with particular focus on recent developments regarding forgetful functors, adjunctions, and their monadic properties. Understand how these theoretical advances contribute to the broader field of mathematical logic and type theory through concrete applications.