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Explore the development of free-forgetful adjunctions between posets and PLTL temporal algebras in this Oxford seminar presentation. Learn how researchers at the Topos Institute approached propositional linear temporal logic by drawing inspiration from free Boolean and Heyting algebras of given sets. Discover the construction and description of induced Eilenberg-Moore categories within this framework. Examine the application of these mathematical structures to temporalize systems and logics through hyperdoctrines, and understand their connection to the stream comonad. Gain insights into future research directions that link this work with the cofree comonad of polynomial functors and the temporalization of doxastic logic, representing collaborative research conducted during summer 2025 at the Topos Institute.
