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Explore the foundational aspects of size and dimension in higher categorical structures through this mathematical seminar presented by Sophie d'Espalungue from IRIF, Paris. Examine the structure and role of universes in formalizing higher categorical structures, working toward a formalization of the hierarchy of the n+1-category of n-categories. Review notions of smallness in higher categorical structures by bringing together perspectives from homotopy type theory and classical categorical intuitions. Investigate how truncation hierarchies, including n-truncated types and n-categories, interact with universes under univalence. Discover connections between Homotopy Type Theory (HoTT) and emerging frameworks for understanding these complex mathematical structures. Focus on the motivations and conceptual aspects of ongoing research in this specialized area of mathematics, presented as part of the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics at Chapman University.
