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Models for $(\infty,n)$-categories with discreteness conditions

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HHHW06 - HHH follow on: Homotopy: fruit of the fertile furrow

There are two ways of turning Segal spaces into models for up-to-homotopy categories, or $(\infty,1)$-categories: either asking that the space of objects be discrete, or requiring Rezk’s completeness condition.  When generalizing to higher $(\infty,n)$-categories, both of these approaches have been taken to multisimplicial models, in the form of Segal $n$-categories and $n$-fold complete Segal spaces, but models given by $\Theta_n$-diagrams have focused on the completeness conditions.  In this talk, we’ll discuss how to get a $\Theta_n$-model with discreteness conditions, but also address the question of when these conditions can be mixed and matched with one another.

This talk is part of the Isaac Newton Institute Seminar Series series.

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