Models for (∞,n)-Categories with Discreteness Conditions

Explore a mathematical lecture that delves into the different approaches for modeling up-to-homotopy categories and (∞,1)-categories through Segal spaces, examining both the discrete object space method and Rezk's completeness condition. Learn how these approaches extend to higher (∞,n)-categories through multisimplicial models, specifically focusing on Segal n-categories and n-fold complete Segal spaces. Discover the development of a Θ_n-model incorporating discreteness conditions and investigate the potential for combining various conditions in these mathematical structures. Gain insights into advanced category theory concepts and their applications in modern mathematics through this hour-long Topos Institute Colloquium presentation.