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Explore advanced category theory concepts in this Topos Institute Colloquium talk focusing on the categorification of Kleisli constructions for pseudomonads. Delve into how the transition from a monad to its category of algebras can be understood through weighted limit and colimit constructions in Cat. Examine the challenges of extending these concepts to the two-dimensional setting, where the 2-category of pseudoalgebras involves Gray-enriched weighted limits. Learn about a novel approach to describing Kleisli categories that successfully categorifies to the pseudomonad setting, and understand how pseudoadjunctions that split the pseudomonad relate to biequivalences and biessentially surjective functors. Gain insights into the development of formal theory of pseudomonads through the lens of tricategorical colimits.
