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Explore the mathematical foundations of 2-classifiers for 2-algebras in this Oxford Seminar presentation that examines work in progress on lifting discrete opfibration classifiers from a 2-category K to the 2-category of algebras of a 2-monad T. Delve into the theoretical framework where discrete opfibration classifiers, functioning as 'Set'-like objects in 2-categories, are extended to algebraic structures through collaborative research with David Jaz Myers. Understand how this work addresses fundamental questions in DOTS (Dynamical and Organizational Theory of Systems) where behavior functors are constructed as 'representables' but lack proper classification without 2-classifiers. Discover the intricate connections between compositionality of functors, properties of algebras they map from, and characteristics of representing objects. Learn about the general phenomena underlying these mathematical structures and examine the tight results obtained regarding the existence conditions for 2-classifiers in 2-algebraic contexts. Gain insights into how this theoretical framework provides a more rigorous foundation for understanding representable functors and their compositional properties within the broader context of categorical algebra and systems theory.
