Higher Category Theory in Cat-Sharp

Explore a mathematical colloquium talk that delves into the double category Cat^#, constructed from polynomial comonads, and its applications in categorical database theory, effects handlers in programming, and discrete open dynamical systems. Learn about the fundamental components of Cat^#, including categories as objects, cofunctors as arrows, and prafunctors as pro-arrows. Discover how monads among prafunctors, such as the free category monad on graphs, have algebras encompassing categories, n-categories, double categories, multicategories, monoids, and monoidal categories. Gain insights into the Cat^# approach for defining higher categories and examine various constructions from higher category theory, including higher categorical nerves and algebraic prafunctors like the free monoidal category monad on Cat.