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Models for homotopical higher categories, Part II

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Julie Bergner
Hongyi Chu & Bruno Stonek
University of Virginia
Mon, 17/08/2020 - 16:30 - 17:45

In this mini-course, we'll review some of the common models for $(\infty,1)$-categories, then discuss the different ways that one can generalize them to obtain models for higher $(\infty,n)$-categories.  We'll primarily consider simplicial models, whose generalizations can be obtained using multi-simplicial diagrams, $\Theta_n$-diagrams, and hybrids thereof.   We'll also look at further variants via mixing and matching the discreteness and completeness conditions used to define Segal categories and complete Segal spaces, respectively, and which combinations actually lead to distinct models.

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