## On truncated quasi-categories

### Alexander Campbell – 19 September 2018

A quasi-category is said to be n-truncated if its hom-spaces are (n-1)-types. In this talk, we will study the model structure for n-truncated quasi-categories, which can be constructed as the Bousfield localisation of Joyal's model structure for quasi-categories at the boundary inclusion of the (n+2)-simplex. Furthermore, we will prove the expected Quillen equivalences between categories and 1-truncated quasi-categories and between n-truncated quasi-categories and Rezk's model for weak (n,1)-categories. This is joint work with Edoardo Lanari.

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