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Keywords:
$n$-categories; $(\infty, n)$-categories; complicial sets; suspension 2-category; pushout of $n$-categories
$n$-categories; $(\infty, n)$-categories; complicial sets; suspension 2-category; pushout of $n$-categories
Summary:
The paper focuses on investigating how certain relations between strict $n$-categories are preserved in a particular implementation of $(\infty, n)$-categories, given by saturated n-complicial sets. In this model, we show that the $(\infty, n)$-categorical nerve of $n$-categories is homotopically compatible with suspension of 1-categories and wedge of $n$-categories. As an application, we show that certain pushouts encoding composition in $n$-categories are homotopy pushouts of saturated $n$-complicial sets.
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